R Studio - Vector Autoregressive Model

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Solution 1. The R codes used to construct logarithmic p is given below dji.raw<-read.csv("https://www.quandl.com/api/v3/datasets/ODA/PSOYB_USD.csv?api_key=K8-6WCWm9UHx18pve3yx&start_date=1995-01-01&end_date=2015-12-31") dji.a <- as.matrix(dji.raw$Value) ts.dji.a <- ts(dji.a,start=c(1988,1),end=c(2015,12),f=12) dji.r <- diff(log(dji.a))*100 ts.dji.r <- ts(dji.r,start=c(1988,2),end=c(2015,12),f=12) # plot DJI average png(file="DJI.png",width=4800,height=2400,res=300) par(mar=c(3,3,1,1),mgp=c(2,.5,0),cex=2) plot(ts.dji.a,type="l",xlab="Year",ylab="DJI",col=4,lwd=3) abline(h=mean(dji.a),col=3,lwd=2,lty=2) The time series plot is given below

4. The autocorrelation plot refers to the series of point plotted on a time function. Here, the lag is fixed to 24 lags and it is found that there is a steady increase from lag 16 onwards till 20 and it starts to decline till 24. The same trend was found in time series plot too 5. The following R code is used to classify the date into two categories and the new variable name is est with the category representation is given below 1 ? Out – of – sample forecasting environment 0? in sample estimation environment R Code: soy$est<- ifelse(as.numeric(as.Date(soy$Date))>= 14610,1,0) Random Walk Model

Linear trend model

Linear trend model with seasonal component

Autoregressive model

7. Going through the various time series plot, we see that there exists some pattern in the dataset. The trend seems to be high during the year end and it started to declines at the start of the year. Thus, there exists seasonal trend in the data. Here, autoregressive model would be more appropriate to predict the pattern as it uses lags in the analysis 8.Vector Autoregressive mode/

9.The Granger causality test is performed between the crude oil prices and the commodity prices. The R output is given below

From the above output, we see that the value of f test statistic is 2.965 and its corresponding p – value is 0.08633. Since the p – value of F test statistic is greater than 0.05, there is no sufficient evidence to conclude that there is a causality between the crude oil prices and the commodity prices 10.Random Walk Model

95% confidence interval Linear trend model

Linear trend model with seasonal component

Autoregressive model

11. The accuracy of the model is given below

12The 10 forecast values is computed and is given below

13.Going through the above analysis, it is found that autoregressive model is the most appropriate forecast to predict the commodity price series. VAR models (vector autoregressive models) are one of the most common models used for multivariate time series. It assumes each variableas a linear function of previous lags of itself and also the past lags of other variables From the above output, we see that the value of f test statistic is 2.965 and its corresponding p – value is 0.08633. Since the p – value of F test statistic is greater than 0.05, there is no sufficient evidence to conclude that there is a causality between the crude oil prices and the commodity prices

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