For this project, you should work with the monthly time series of the assigned commodity prices, spanning from January of 1995 to December of 2015.

The project consists of a set of time series estimation and forecasting exercises, pre-sented in a list of assignments below. You should address all these items. You should submit a hard copy of the report, and also send me an R file, containing all the coding for your project.

1. Calculate real prices from the obtained nominal prices. using U.S. producer price index as a deflator, and transform these real prices to the natural logarithm. From here forward, work with these transformed time series of commodity prices, denoted by p1.

2. Plot the time series.

3. Plot the autocorrelogram for up to 24 lap.

4. Based on your observations from 2-3, discuss any apparent features of the time series.

5. Divide the series into the in-sample estimation environment (observations up to and including Dec 2009) and the out-of-sample forecasting environ¬ment (observations beginning from Jan 2010 and onwards).

6. Using in-sample observations to obtain parameter estimates, calculate and plot point forecasts (for the duration equivalent to the out-of-sample window size) and the associated 95% interval forecasts using the following models:

(a) random walk:

(b) linear (deterministic) trend model:

(c) linear (deterministic) trend model with seasonal component;

(d) autoregressive models of orders 1 through 6.

7. Based on your observations from 6, discuss any (additional) characteristics of the time series, particularly in terms of their apparent dynamics.

8. Using in-sample observations (again), estimate vector autoregressive model of orders 1 through 6, where the vector of variables is given by x, = (p,,r,)', and where r, is natural logarithm of the real crude oil prices.

9. Test for in-sample Granger causality between the crude oil prices and the commodity prices in the considered vector autoregressive models.

10. Within the rolling forecasting environment, generate one-step-ahead fore-casts throughout the out-of-sample set using the following models:

(a) random walk;
(b) linear (deterministic) trend model with seasonal component;
(c) autoregressive model of order p, where the optimal p is selected based on AIC (or BIC);
(d) vector autoregressive model of order p. where the optimal pis the same as above.

11. For all the aforementioned models:

(a) obtain one-step ahead forecast errors, and calculate and report the out-of-sample root mean square forecast error (FINISFE) measures:

(b) test the hypotheses of (i) error unbiasedness; (ii) error efficiency; and (iii) no autocorrelation.

12. Combine forecasts from 10 using the equal-weights scheme, and calculate and report the associated out-of-sample RIVSFE measure.

13. Based on your observations from 10 and 11:

(a) discuss which of the considered models is preferred in terms of accu¬rate forecasting of the commodity price series.

(b) is there evidence of out-of-sample Granger causality between the crude oil prices and the commodity prices?

# clean up the working space (not necessary, but can be a good practice)
rm(list=ls())
gc()

# download the Soybeans price Index (internet connection is necessary) <- read.csv("https://www.quandl.com/api/v3/datasets/ODA/PSOYB_USD.csv?api_key=K8-6WCWm9UHx18pve3yx&end_date=2016-08-30")
soy <- 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")

# download the producer price index (internet connection is necessary)
index <- read.csv("https://www.quandl.com/api/v3/datasets/FRED/PPIACO.csv?api_key=9acm7DjKwub3xaFHzp4o&collapse=monthly&start_date=1994-12-31&end_date=2015-12-31")

## soybeans Average
soy.a <- as.matrix(soy$Value)
ts.soy.a <- ts(soy.a,start=c(1995,1),end=c(2015,12),f=12)

## index Average
index.a <- as.matrix(index$VALUE)
ts.index.a <- ts(index.a,start=c(1995,1),end=c(2015,12),f=12)

#Q1
##calculate real price
soy.real <- soy.a/index.a
##transform to natural logarithm, get pt
p <- log(soy.real)

#Q2
##transform data to time series format
ts.p <- ts(p,start=c(1995,1),end=c(2015,12),f=12)
summary(ts.p)
##plot time series
par(mar=c(3,3,1,1),mgp=c(2,.5,0),cex=2)
plot(ts.p,type="l",xlab="Year",ylab="log real soybeans price",col=4,lwd=2)
abline(h=mean(ts.p),col=2,lwd=2,lty=2)