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Question on regression (AR model)?

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Louise
Louise on 3 Jan 2013
Closed: MATLAB Answer Bot on 20 Aug 2021
I have some historical data RV that I want to fit a model to. The model is:
RV(t+1) = C0 + C1*RV(t) + C2*RV_weekAverage(t-5) + C3*RV_monthAverage(t-30) + e
where the future RV depends on the previous RV and averages of some previous RV values.
t - is time
C0, C1, C2, C3 - are parameters to be determined
RV_weekAverage = (1/5)*(sum of RVs from t-1 to t-5)
RV_monthAverage = (1/30)*(sum of RVs from t-1 to t-30)
e - error
I think I am supposed to use an AR model but I am not exactly sure how to implement it since for an AR model the right-hand side don't have averages but simple previous values such as:
RV(t+1) = C0 + C1*RV(t) + C2*RV(t-1) + e
To use the AR model, I would have to try:
RV(t+1) = C0 + C1*RV(t) + C2*(1/5)*[RV(t-1)+...+RV(t-5)] + C3*(1/30)*[RV(t-1)+...+RV(t-30)] + e
I am not sure how to include the factor of (1/5) or (1/30) into the model without interfering with the parameters C0, C1, C2, and C3 when I try to estimate them. This is all I have so far:
model = arima(6,0,0)
fit = estimate(model,RV)

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