R-ARIMA parameters. How to determine arima (p,d,q) parameters?

Question

I have weekly data values extracted from google trends and I want to apply time series in R for predicting future values. I have tried using auto.arima() but the results seem to be only one constant value for all future prediction, and if i manually give random parameters in arima(c(p,d,q)), I am getting various types of results. So how to determine appropriate values for my data.

data2<-ts(data$Volume)
[1]  64  74  64  68 100  87  79  72  66  74  58  68  65  71  71  71  63  65 62  58  58
[22]  58  58  60  56  51  56  52  58  59  58  60  66  67  69  67  80  66  73  73  72  68
[43]  66  70  69  66  68  67  60  50  36  50
fit<-auto.arima(data2)
pred<-predict(fit,n.ahead=30, interaval="prediction", se.fit="FALSE") 
plot(pred)
pred

fit<-arima(data2,c(3,1,1)
pred<-predict(fit,n.ahead=30, interaval="prediction", se.fit="FALSE") 
plot(pred)
pred

Answer 1

This answer assumes you know what the parameters (p,d and q) mean, if not, you need to do some reading. Now, there are two set of parameters to be supplied in an ARIMA call: trend and seasonal.

1. First find out whether your data has any trend or seasonality by simply plotting the time-series, or using decompose function

2. When you have idea of whether there is need for trend and/or seasonal differencing, you can try some values for the d and/or D parameter and visualize the differenced series to decide appropriate value. Or, you can do ACF on the differenced series and stop before the correlations end up starting with a negative value.

3. Now, do ACF and PACF plotting on the differenced(stationary) series. Identify till what lags do you want to keep for AR/MA terms. Usually keeping either one of them to a non-zero value should be okay. As a rule of thumb, if ACF falls rapidly to negative values, use MA, else if it falls gradually, use AR.

Answer 2

It is showing a straight line since your data does not appear to be correlated.

run:

pacf(dat2)

no lagged values are showing significant correlation and that is also shown in the fit that the auto.arima chose. Looking at the subset of data that you have given it doesn't look like ARIMA will be a good choice of model for this data.

Answer 3

you have to pick the best fit sarima model first by looking at ACF and Residuals plot or taking the arima model with least AIC, then you can predict with function: m=predict(fit,n.ahead= ). then use m$pred to find future predictions and m$se to find its upper and lower limits.