nortsTest (version 1.0.3)

Lm.test: 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)

Value

a h.test class with the main results of the Lagrage multiplier hypothesis test. The h.test class have the following values:

• "Lm"The lagrange multiplier statistic

• "df"The test degrees freedoms

• "p.value"The p value

• "alternative"The alternative hypothesis

• "method"The used method

• "data.name"The data name.

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.

Author

A. Trapletti and Asael Alonzo Matamoros

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.

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)