I'm having trouble doing a forecast based on previous data. I have data that represents eight years worth of monthly data $(n=96)$, for number of sales. I want to forecast the next 12 months based on this data using an optimal linear forecast, and I want to provide the variance of this forecast.
Here is the data
-1.96
-2.3
-2.61
-2.62
-2.38
-1.9
-1.35
-0.98
-0.65
-0.53
-0.82
-1.19
-1.39
-1.19
-0.93
-1.11
-1.51
-1.8
-1.43
-0.79
0.05
0.36
0.58
0.44
-0.15
-0.88
-1.54
-1.93
-2.18
-1.88
-1.43
-1.15
-1.48
-1.47
-1.24
-0.97
-0.65
-0.37
-0.24
-0.07
-0.09
0.4
0.83
0.98
0.96
0.29
-0.13
-0.94
-1.16
-0.37
0.05
0.18
-0.53
-0.91
-1.11
-1.28
-1.34
-1.64
-1.06
-0.15
0.34
0.14
0.42
0.44
0.05
-0.83
-1.54
-1.58
-1.27
-1.58
-1.37
-0.74
-0.72
-0.77
-1.21
-1.8
-1.74
-1.3
-0.56
0.15
0.86
1.39
2.05
2.24
2.08
1.58
1.23
0.64
0.34
0.34
0.71
1.23
1.69
1.78
2.03
2.13
I want to forecast this using either an AR, MA, or ARMA model in R but am not completely sure how to approach this. I know I need to estimate the autocovariance matrix, and I will make the assumption that the autocovariance is zero at lag h > 36. I'm also struggling with what order of the model to use.