Lm.test {nortsTest}

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

y

a numeric vector or an object of the ts class containing a stationary time series.

lag.max

an integer with the number of used lags.

alpha

Level of the test, possible values range from 0.01 to 0.1. By default alpha = 0.05 is used.

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:

statistic:

the Lagrange multiplier statistic.

parameter:

the test degrees freedoms.

p.value:

the p value.

alternative:

a character string describing the alternative hypothesis.

method:

a character string “Lagrange Multiplier test”.

data.name:

a character string giving the name of the data.

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)