'Assessing Normality of a Stationary Process.'

Description

Despite that several tests for normality in stationary processes have been proposed in the literature, consistent implementations of these tests in programming languages are limited.Seven normality test are implemented. The asymptotic Lobato and Velasco's, asymptotic Epps, Psaradakis and Vávra, Lobato and Velasco's sieve bootstrap approximation, El bouch et al., Epps sieve bootstrap approximation and the random projections tests for univariate stationary process. Some other diagnostics such as, unit root test for stationarity, seasonal tests for seasonality, and arch effect test for volatility; are also performed. Additionally, the El bouch test performs normality tests for bivariate time series. The package also offers residual diagnostic for linear time series models developed in several packages.

Details

We present several functions for testing the hypothesis of normality in univariate stationary processes, the epps.test, lobato.test, rp.test, lobato-bootstrap.test, epps-bootstrap.test, elbouch.test, and varvra.test. Additionally, the elbouch.test function performs a bivariate normality test when the user provides a second time series. For model diagnostics, we provide functions for unit root, seasonality and ARCH effects tests for stationary, and other methods for visual checks using the ggplot2 and forecast packages.

References

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.https://projecteuclid.org/euclid.aos/1176350618.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689. doi:https://doi.org/10.1017/S0266466604204030.

Psaradakis, Z. & Vávra, M. (2017). A distance test of normality for a wide class of stationary process. Journal of Econometrics and Statistics. 2, 50-60. doi:https://doi.org/10.1016/j.ecosta.2016.11.005

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Hyndman, R. & Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R. Journal of Statistical Software. 26(3), 1-22.doi: 10.18637/jss.v027.i03.

Wickham, H. (2008). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York.

The Lagrange Multiplier test for arch effect.

Description

Performs the Lagrange Multipliers test for homoscedasticity in a stationary process. The null hypothesis (H0), is that the process is homoscedastic.

Usage

Lm.test(y,lag.max = 2,alpha = 0.05)

Arguments

Details

The Lagrange Multiplier test proposed by Engle (1982) fits a linear regression model for the squared residuals and examines whether the fitted model is significant. So the null hypothesis is that the squared residuals are a sequence of white noise, namely, the residuals are homoscedastic.

Value

A list with class "h.test" containing the following components:

Author(s)

A. Trapletti and Asael Alonzo Matamoros.

References

Engle, R. F. (1982). Auto-regressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica. 50(4), 987-1007.

McLeod, A. I. and W. K. Li. (1984). Diagnostic Checking ARMA Time Series Models Using Squared-Residual Auto-correlations. Journal of Time Series Analysis. 4, 269-273.

See Also

arch.test

Examples

# generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
Lm.test(y)

The ARCH effect test function.

Description

Performs the Pormanteau Q and Lagrange Multipliers test for homoscedasticity in a univariate stationary process. The null hypothesis (H0), is that the process is homoscedastic.

Usage

arch.test(y, arch = c("box","Lm"), alpha = 0.05, lag.max = 2)

Arguments

Details

Several different tests are available: Performs Portmanteau Q and Lagrange Multiplier tests for the null hypothesis that the residuals of an ARIMA model are homoscedastic. The ARCH test is based on the fact that if the residuals (defined as e(t)) are heteroscedastic, the squared residuals (e^2[t]) are autocorrelated. The first type of test is to examine whether the squares of residuals are a sequence of white noise, which is called the Portmanteau Q test, and similar to the Ljung-Box test on the squared residuals. By default, alpha = 0.05 is used to select the more likely hypothesis.

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros

References

Engle, R. F. (1982). Auto-regressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica. 50(4), 987-1007.

McLeod, A. I. & W. K. Li. (1984). Diagnostic Checking ARMA Time Series Models Using Squared-Residual Auto-correlations. Journal of Time Series Analysis. 4, 269-273.

See Also

normal.test, seasonal.test, uroot.test

Examples

#  stationary  ar process
y = arima.sim(100,model = list(ar = 0.3))
arch.test(y)

Automatically create a ggplot for time series objects.

Description

autoplot takes an object of type ts or mts and creates a ggplot object suitable for usage with stat_forecast.

Usage

## S3 method for class 'ts'
autoplot(
  object,
  series = NULL,
  xlab = "Time",
  ylab = deparse(substitute(object)),
  main = NULL,
  facets = FALSE,
  colour = TRUE,
  ...
)

## S3 method for class 'numeric'
autoplot(
  object,
  series = NULL,
  xlab = "Time",
  ylab = deparse(substitute(object)),
  main = NULL,
  ...
)

## S3 method for class 'ts'
fortify(model, data, ...)

Arguments

Details

fortify.ts takes a ts object and converts it into a data frame (for usage with ggplot2).

Value

None. Function produces a ggplot2 graph.

Author(s)

Mitchell O'Hara-Wild

See Also

plot.ts, fortify

Examples

library(ggplot2)
autoplot(USAccDeaths)

lungDeaths <- cbind(mdeaths, fdeaths)
autoplot(lungDeaths)
autoplot(lungDeaths, facets=TRUE)

Generic function for a visual check of residuals in time series models.

Description

Generic function for a visual check of residuals in time series models, these methods are inspired in the check.residuals function provided by the forecast package.

Usage

## S3 method for class 'ts'
check_plot(y, model = " ", ...)

Arguments

Value

A graph object from ggplot2.

Author(s)

Asael Alonzo Matamoros.

See Also

check_residuals

Examples

y = arima.sim(100,model = list(ar = 0.3))
check_plot(y)

Generic functions for checking residuals in time series models

Description

Generic function for residuals check analysis, these methods are inspired in the check.residuals function provided by the forecast package.

Usage

## S3 method for class 'ts'
check_residuals(
  y,
  normality = "epps",
  unit_root = NULL,
  seasonal = NULL,
  arch = NULL,
  alpha = 0.05,
  plot = FALSE,
  ...
)

Arguments

Details

The function performs a residuals analysis, it prints a unit root and seasonal test to check stationarity, and a normality test for checking Gaussian distribution. In addition, if the plot option is TRUE a time plot, ACF, and histogram of the series are presented.

Value

The function does not return any value

Author(s)

Asael Alonzo Matamoros

References

Dickey, D. & Fuller, W. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 74, 427-431.

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.http://www.jstor.org/stable/2336512. doi:10.1214/aos/1176350618

Osborn, D., Chui, A., Smith, J., & Birchenhall, C. (1988). Seasonality and the order of integration for consumption. Oxford Bulletin of Economics and Statistics. 50(4), 361-377.

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
check_residuals(y,unit_root = "adf")

The Sieve Bootstrap Cramer Von Mises test for normality.

Description

Performs the approximated Cramer Von Mises test of normality for univariate time series. Computes the p-value using Psaradakis and Vavra's (2020) sieve bootstrap procedure.

Usage

cvm_bootstrap.test(y, reps = 1000, h = 100, seed = NULL)

Arguments

Details

Employs Cramer Von Mises test approximating the p-value using a sieve-bootstrap procedure, Psaradakis, Z. and Vávra, M. (2020).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Bulmann, P. (1997). Sieve Bootstrap for time series. Bernoulli. 3(2), 123 -148.

Stephens, M.A. (1986): Tests based on EDF statistics. In: D'Agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.

See Also

vavra.test, sieve.bootstrap

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
cvm_bootstrap.test(y)

Computes El Bouch, et al.'s z statistic.

Description

Computes the El Bouch, Michel, & Comon's z test statistic for normality of a univariate or bivariate time series.

Usage

elbouch.statistic(y, x = NULL)

Arguments

Details

This function computes Mardia's standardized 'z = (B - E_B)/ sd_B' statistic corrected by El Bouch, et al. (2022) for stationary bivariate time series. Where: 'B' is the square of a quadratic form of the process 'c(y, x)'; 'E_B' and 'sd_B' are the estimator's expected value and standard error respectively. If 'x' is set to 'NULL', the test computes the univariate counterpart.

Value

a real value with El Bouch test's statistic.

Author(s)

Asael Alonzo Matamoros.

References

El Bouch, S., Michel, O. & Comon, P. (2022). A normality test for Multivariate dependent samples. Journal of Signal Processing. Volume 201.

Mardia, K. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57 519-530

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.statistic

Examples

# Genere an univariate stationary ARMA process
y = arima.sim(100,model = list(ar = 0.3))
elbouch.statistic(y)

# Generate a bivariate Gaussian random vector
x = rnorm(200)
y = rnorm(200)
elbouch.statistic(y = y, x = x)

Computes El Bouch, et al.'s test for normality of multivariate dependent samples.

Description

Computes the El Bouch, Michel, & Comon's test for normality of a bivariate dependent samples.

Usage

elbouch.test(y, x = NULL)

Arguments

Details

This function computes El Bouch, et al. (2022) test for normality of bivariate dependent samples. If 'x' is set to 'NULL', the test computes the univariate counterpart. This test is a correction of Mardia's, (1970) multivariate skewness and kurtosis test for multivariate samples.

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros.

References

El Bouch, S., Michel, O. & Comon, P. (2022). A normality test for Multivariate dependent samples. Journal of Signal Processing. Volume 201.

Mardia, K. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57 519-530

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.test

Examples

# Generate an univariate stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
elbouch.test(y)

# Generate a bivariate Gaussian random vector
x = rnorm(200)
y = rnorm(200)
elbouch.test(y = y, x = x)

Estimates the Epps statistic.

Description

Estimates the Epps statistic minimizing the quadratic loss of the process' characteristic function in terms of the first two moments.

Usage

epps.statistic(y, lambda = c(1,2))

Arguments

Details

The Epps test minimize the process' empirical characteristic function using a quadratic loss in terms of the process two first moments. Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014) upgrade the test implementation by allowing the option of evaluating the characteristic function with random values.

This function is the equivalent of Sub in Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). This function uses a quadratic optimization solver implemented by Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007).

Value

a real value with the Epps test's statistic.

Author(s)

Alicia Nieto-Reyes and Asael Alonzo Matamoros.

References

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007). Numerical Recipes. The Art of Scientific Computing. Cambridge University Press.

See Also

lobato.statistic

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
epps.statistic(y)

The asymptotic Epps and Pulley Test for normality.

Description

Performs the asymptotic Epps test of normality for univariate time series. Computes the p-value using the asymptotic Gamma Distribution.

Usage

epps.test(y, lambda = c(1,2))

Arguments

Details

The Epps test minimize the process' empirical characteristic function using a quadratic loss in terms of the process two first moments. Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014) upgrade the test implementation by allowing the option of evaluating the characteristic function with random values. The amoebam() function of Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007), performs the optimal search.

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007). Numerical Recipes. The Art of Scientific Computing. Cambridge University Press.

See Also

lobato.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
epps.test(y)

# Epps tests with random lambda values
y = arima.sim(100,model = list(ar = c(0.3,0.2)))
epps.test(y, lambda = rnorm(2,mean = 1,sd = 0.1))

The Sieve Bootstrap Epps and Pulley test for normality.

Description

Performs the approximated Epps and Pulley's test of normality for univariate time series. Computes the p-value using Psaradakis and Vavra's (2020) sieve bootstrap procedure.

Usage

epps_bootstrap.test(y, lambda = c(1,2), reps = 500, h = 100, seed = NULL)

Arguments

Details

The Epps test minimize the process' empirical characteristic function using a quadratic loss in terms of the process two first moments, Epps, T.W. (1987). Approximates the p-value using a sieve-bootstrap procedure Psaradakis, Z. and Vávra, M. (2020).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

See Also

lobato.statistic, epps.test

Examples

# Generating an stationary arma process
y = arima.sim(300, model = list(ar = 0.3))
epps_bootstrap.test(y, reps = 1000)

acf plot.

Description

Plot of the auto-correlation function for a univariate time series.

Usage

ggacf(y, title = NULL)

Arguments

Value

None.

Author(s)

Asael Alonzo Matamoros

Examples

x = rnorm(100)
ggacf(x)

Histogram with optional normal density functions.

Description

Plots a histogram and density estimates using ggplot.

Usage

gghist(y, title = NULL, xlab = NULL, ylab = "counts", bins, add.normal = TRUE)

Arguments

Value

None.

Author(s)

Rob J Hyndman

Examples

x = rnorm(100)
gghist(x,add.normal = TRUE)

qqplot with normal qqline

Description

Plot the quantile-quantile plot and quantile-quantile line using ggplot.

Usage

ggnorm(y, title = NULL, add.normal = TRUE)

Arguments

Value

None.

Author(s)

Asael Alonzo Matamoros

Examples

x = rnorm(100)
ggnorm(x)

pacf plot.

Description

Plot of the partial autocorrelation function for a univariate time series.

Usage

ggpacf(y, title = NULL)

Arguments

Value

None.

Author(s)

Mitchell O'Hara-Wild and Asael Alonzo Matamoros

Examples

x = rnorm(100)
ggpacf(x)

The Sieve Bootstrap Jarque-Bera test for normality.

Description

Performs the approximated Jarque Bera test of normality for univariate time series. Computes the p-value using Psaradakis and Vavra's (2020) sieve bootstrap procedure.

Usage

jb_bootstrap.test(y, reps = 1000, h = 100, seed = NULL)

Arguments

Details

Employs Jarque Bera skewness-kurtosis test approximating the p-value using a sieve-bootstrap procedure, Psaradakis, Z. and Vávra, M. (2020).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Bulmann, P. (1997). Sieve Bootstrap for time series. Bernoulli. 3(2), 123 -148.

J. B. Cromwell, W. C. Labys and M. Terraza (1994): Univariate Tests for Time Series Models, Sage, Thousand Oaks, CA, pages 20–22.

See Also

vavra.test, sieve.bootstrap

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
jb_bootstrap.test(y)

Computes the Lobato and Velasco statistic.

Description

Computes the Lobato and Velasco's statistic. This test proves a normality assumption in correlated data employing the skewness-kurtosis test statistic, but studentized by standard error estimates that are consistent under serial dependence of the observations.

Usage

lobato.statistic(y, c = 1)

Arguments

Details

This function is the equivalent of GestadisticoVn of Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

A real value with the Lobato and Velasco test's statistic.

Author(s)

Alicia Nieto-Reyes and Asael Alonzo Matamoros.

References

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

See Also

epps.statistic

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
lobato.statistic(y,3)

The asymptotic Lobato and Velasco's Test for normality.

Description

Performs the asymptotic Lobato and Velasco's test of normality for univariate time series. Computes the p-value using the asymptotic Gamma Distribution.

Usage

lobato.test(y,c = 1)

Arguments

Details

This test proves a normality assumption in correlated data employing the skewness-kurtosis test statistic, but studentized by standard error estimates that are consistent under serial dependence of the observations. The test was proposed by Lobato, I., & Velasco, C. (2004) and implemented by Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

See Also

lobato.statistic,epps.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
lobato.test(y)

The Sieve Bootstrap Lobato and Velasco's Test for normality.

Description

Performs the approximated Lobato and Velasco's test of normality for univariate time series. Computes the p-value using Psaradakis and Vavra's (2020) sieve bootstrap procedure.

Usage

lobato_bootstrap.test(y, c = 1, reps = 1000, h = 100, seed = NULL)

Arguments

Details

This test proves a normality assumption in correlated data employing the skewness-kurtosis test statistic proposed by Lobato, I., & Velasco, C. (2004), approximating the p-value using a sieve-bootstrap procedure, Psaradakis, Z. and Vávra, M. (2020).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.statistic,epps.test

Examples

# Generating an stationary arma process
y = arima.sim(1000,model = list(ar = 0.3))
lobato_bootstrap.test(y, reps = 1000)

The normality test for stationary process

Description

Perform a normality test. The null hypothesis (H0) is that the given data follows a stationary Gaussian process.

Usage

normal.test(y, normality = c("epps","lobato","vavra","rp","jb","ad","shapiro"),
                    alpha = 0.05)

Arguments

Details

"lobato", "epps", "vavras" and "rp" test are for testing normality in stationary process. "jb", "ad", and "shapiro" tests are for numeric data. In all cases, the alternative hypothesis is that y follows a Gaussian process. By default, alpha = 0.05 is used to select the more likely hypothesis.

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros

References

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

Psaradakis, Z. & Vávra, M. (2017). A distance test of normality for a wide class of stationary process. Journal of Econometrics and Statistics. 2, 50-60.

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Patrick, R. (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Journal of Applied Statistics. 31, 115-124.

Cromwell, J. B., Labys, W. C. & Terraza, M. (1994). Univariate Tests for Time Series Models. Sage, Thousand Oaks, CA. 20-22.

See Also

uroot.test, seasonal.test

Examples

#  stationary  ar process
y = arima.sim(100, model = list(ar = 0.3))
normal.test(y) # epps test

# normal random sample
y = rnorm(100)
normal.test(y, normality = "shapiro")

# exponential random sample
y = rexp(100)
normal.test(y, normality = "ad")

Generate a random projection.

Description

Generates a random projection of a univariate stationary stochastic process. Using a beta(shape1,shape2) distribution.

Usage

random.projection(y,shape1,shape2,seed = NULL)

Arguments

Details

Generates one random projection of a stochastic process using a beta distribution. For more details, see: Nieto-Reyes, A.,Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

a real vector with the projected stochastic process.

Author(s)

Alicia Nieto-Reyes and Asael Alonzo Matamoros.

References

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.Result

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.test epps.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
rp.test(y)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

ggplot2

autoplot

Generates a test statistics sample of random projections.

Description

Generates a 2k sample of test statistics projecting the stationary process using the random projections procedure.

Usage

rp.sample(y, k = 1, pars1 = c(100,1), pars2 = c(2,7), seed = NULL)

Arguments

Details

The rp.sample function generates '2k' tests statistics by projecting the time series using '2k' stick breaking processes. First, the function samples 'k' stick breaking processes using pars1 argument. Then, projects the time series using the sampled stick processes. Later, applies the Epps statistics to the odd projections and the Lobato and Velasco’s statistics to the even ones. Analogously, the function performs the three steps using also pars2 argument

The function uses beta distributions for generating the '2k' random projections. By default, uses a beta(shape1 = 100,shape = 1) distribution contained in pars1 argument to generate the first 'k' projections. For the later 'k' projections the functions uses a beta(shape1 = 2,shape = 7) distribution contained in pars2 argument.

The test was proposed by Nieto-Reyes, A.,Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

A list with 2 real value vectors:

Author(s)

Alicia Nieto-Reyes and Asael Alonzo Matamoros

References

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.test, epps.test

Examples

# Generating an stationary ARMA process
y = arima.sim(100,model = list(ar = 0.3))
rp.sample(y)

The k random projections test for normality.

Description

Performs the random projection test for normality. The null hypothesis (H0) is that the given data follows a stationary Gaussian process.

Usage

rp.test(y, k = 1, FDR = TRUE, pars1 = c(100,1), pars2  = c(2,7),
               seed = NULL)

Arguments

Details

The random projection test generates '2k' random projections of 'y'. Applies Epps statistics to the odd projections and Lobato and Velasco’s statistics to the even ones. Computes the '2k' p.values using an asymptotic chi-square distribution with two degrees of freedom. Finally, mixes the p.values using a false discover rate procedure. By default, mixes the p.values using Benjamin and Yekutieli’s (2001) method.

The function uses beta distributions for generating the '2k' random projections. By default, uses a beta(shape1 = 100,shape = 1) distribution contained in pars1 argument to generate the first 'k' projections. For the later 'k' projections the functions uses a beta(shape1 = 2,shape = 7) distribution contained in pars2 argument.

The test was proposed by Nieto-Reyes, A.,Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics. 29, 1165–1188. Doi:10.1214/aos/1013699998.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika. 75, 800–803. Doi:10.2307/2336325.

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

See Also

lobato.test, epps.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
rp.test(y)

The Seasonal unit root tests function

Description

Perform a seasonal unit root test to check seasonality in a linear stochastic process

Usage

seasonal.test(y, seasonal = c("ocsb","ch","hegy"), alpha = 0.05)

Arguments

Details

Several different tests are available: In the kpss test, the null hypothesis that y has a stationary root against a unit-root alternative. In the two remaining tests, the null hypothesis is that y has a unit root against a stationary root alternative. By default, alpha = 0.05 is used to select the more likely hypothesis.

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros

References

Osborn, D., Chui, A., Smith, J., & Birchenhall, C. (1988). Seasonality and the order of integration for consumption. Oxford Bulletin of Economics and Statistics. 50(4), 361-377.

Canova, F. & Hansen, B. (1995). Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability. Journal of Business and Economic Statistics. 13(3), 237-252.

Hylleberg, S., Engle, R., Granger, C. & Yoo, B. (1990). Seasonal integration and cointegration. Journal of Econometrics 44(1), 215-238.

See Also

normal.test, uroot.test

Examples

#  stationary  ar process
y = ts(rnorm(100),frequency = 6)
seasonal.test(y)

The Sieve Bootstrap Shapiro test for normality.

Description

Performs the approximated Shapiro test for normality for univariate time series. Computes the p-value using Psaradakis and Vavra's (2020) sieve bootstrap procedure.

Usage

shapiro_bootstrap.test(y, reps = 1000, h = 100, seed = NULL)

Arguments

Details

Employs the Shapiro test approximating the p-value using a sieve-bootstrap procedure, Psaradakis, Z. and Vávra, M. (2020).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Bulmann, P. (1997). Sieve Bootstrap for time series. Bernoulli. 3(2), 123 -148.

Patrick Royston (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Applied Statistics, 31, 115–124. Doi:10.2307/2347973.

See Also

vavra.test, sieve.bootstrap

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
jb_bootstrap.test(y)

Generates a sieve bootstrap sample.

Description

The function generates a sieve bootstrap sample for a univariate linear stochastic process.

Usage

sieve.bootstrap(y,reps = 1000,pmax = NULL,h = 100,seed = NULL)

Arguments

Details

simulates bootstrap samples for the stochastic process y, using a stationary auto-regressive model of order "pmax", AR(pmax). If pmax = NULL (default), the function estimates the process maximum lags using an AIC as a model selection criteria.

Value

A matrix or reps row and n columns, with the sieve bootstrap sample and n the time series length.

Author(s)

Asael Alonzo Matamoros.

References

Bulmann, P. (1997). Sieve Bootstrap for time series. Bernoulli. 3(2), 123 -148.

See Also

lobato.test, epps.test.

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
M = sieve.bootstrap(y)

The Unit root tests function.

Description

Perform a unit root test to check stationary in a linear stochastic process.

Usage

uroot.test(y, unit_root = c("adf","kpss","pp","box"), alpha = 0.05)

Arguments

Details

Several different tests are available: In the kpss test, the null hypothesis that y has a stationary root against a unit-root alternative. In the two remaining tests, the null hypothesis is that y has a unit root against a stationary root alternative. By default, alpha = 0.05 is used to select the more likely hypothesis.

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros and A. Trapletti.

References

Dickey, D. & Fuller, W. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 74, 427-431.

Kwiatkowski, D., Phillips, P., Schmidt, P. & Shin, Y. (1992). Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root, Journal of Econometrics. 54, 159-178.

Phillips, P. & Perron, P. (1988). Testing for a unit root in time series regression, Biometrika. 72(2), 335-346.

Ljung, G. M. & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika. 65, 297-303.

See Also

normal.test, seasonal.test

Examples

#  stationary  ar process
y = arima.sim(100,model = list(ar = 0.3))
uroot.test(y)

# a random walk process
y = cumsum(y)
uroot.test(y, unit_root = "pp")

Vávra test's sieve Bootstrap sample for Anderson Darling statistic

Description

Generates a sieve bootstrap sample of the Anderson-Darling statistic test.

Usage

vavra.sample(y, normality = c("ad","lobato","jb","cvm","shapiro","epps"),
                    reps = 1000, h = 100, seed = NULL, c = 1, lambda = c(1,2))

Arguments

Details

The Vávra test approximates the empirical distribution function of the Anderson-Darlings statistic, using a sieve bootstrap approximation. The test was proposed by Psaradakis, Z. & Vávra, M (20.17).

This function is the equivalent of xarsieve of Psaradakis, Z. & Vávra, M (20.17).

Value

A numeric array with the Anderson Darling sieve bootstrap sample

Author(s)

Asael Alonzo Matamoros.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Psaradakis, Z. & Vávra, M. (2017). A distance test of normality for a wide class of stationary process. Journal of Econometrics and Statistics. 2, 50-60.

Bulmann, P. (1997). Sieve Bootstrap for time series. Bernoulli. 3(2), 123 -148.

See Also

epps.statistic, lobato.statistic

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
adbs = vavra.sample(y)
mean(adbs)

The Psaradakis and Vávra test for normality.

Description

Performs the Psaradakis and Vávra distance test for normality. The null hypothesis (H0), is that the given data follows a Gaussian process.

Usage

vavra.test(y, normality = c("ad","lobato","jb","cvm","epps"),
                  reps = 1000, h = 100, seed = NULL, c = 1, lambda = c(1,2))

Arguments

Details

The Psaradakis and Vávra test approximates the empirical distribution function of the Anderson Darling's statistic, using a sieve bootstrap approximation. The test was proposed by Psaradakis, Z. & Vávra, M. (20.17).

Value

A list with class "h.test" containing the following components:

Author(s)

Asael Alonzo Matamoros.

References

Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.

Psaradakis, Z. & Vávra, M. (2017). A distance test of normality for a wide class of stationary process. Journal of Econometrics and Statistics. 2, 50-60.

Bulmann, P. (1997). Sieve Bootstrap for time series. Bernoulli. 3(2), 123 -148.

See Also

lobato.test, epps.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
vavra.test(y)