Please explain why: please answer both questions 1. The order (p) of a autogress
ID: 3310647 • Letter: P
Question
Please explain why: please answer both questions
1. The order (p) of a autogressiove(AR) process best be determined by the :
Durbin-Watson Statistic
Box Piece Chi-square statistic
Autocorrelation function
Partial autocorrelation fuction coeficcents to be significant at lagged p
all of the above
2.What is the null hypthesis being tested using the ljung or box pierce statistic?
The set of autocorrelations of residuals is jointly equal to zero
The set of autocorrelations are jointly not equal to zero
The set of autocorrelations are jointly equal to one
The set of autocorrelations are jointly not equal to one
All of the above
Explanation / Answer
1. The order (p) of an Autoregressive (AR) process is best determined by:
Partial autocorrelation function co-efficients to be significant at lagged p
Explanation:
Among the choices,
The Durbin Watson statistic is a test for autocorrelation in the residuals of a TS regression (closer to 0 indicates high positive auto-correlation, closer to 4 indicates high negative auto-correlation, closer to 2 indicates little or no autocorrelation). This doesn't attempt to examine the specific lag 'p' which may/may not exhibit auto-correlation.
The Box piece test is also something to test the hypothesis about the autocorrelation of the time series being different from zero (=0 is the null hypothesis). This also tests the model's autocorrelation based on a specific no. of lags and 'NOT' at specific lag 'p'.
The Autocorrelatin function ACF is used to determine the autocorrelation of a model with its lagged self. Here again, the effects of other lags are not controlled for. ACF is used to determine order of Moving Average MA models
PACF or the Partial autocorrelation function presents the correlation between a time series and each of its intermediate lagged values. This allows for obtaining the partial correlation of a time series with its own lagged values by controlling for the values of the time series at all shorter lags.
Hence, an AR model's order is best identified with the PACF. For an AR model, the PACF shuts off after lag 'p' which becomes the order making it the AR(p) model. Here, 'shuts off' implies that the partial autocorrelations are equal to 0, beyond the lag p. i.e., the number of non-zero partial autocorrelations p gives the order of the AR model.
2) The null hypothesis being tested using the Ljung Box or the Box-Pierce test is that the residuals from the ARIMA model have no autocorrelation. i.e., The set of autocorrelations of residuals is jointly equal to Zero
None of the other options mention Residuals which is where Ljung box test is used in case of ARIMA models apart from its standard use as a test of identifying if any combinations in a group of autocorrelations of a time series are different from zero.