Data analysis - commodity prices

Making money in commodities is not easy. Most commodities traders lose money rather than make it. The package astsa includes the data set chicken, which is the monthly whole bird spot price, Georgia docks, US cents per pound, from August, 2001 to July, 2016.

The astsa package is preloaded in your R console and the data are plotted for you, note the trend and seasonal components.

First, you will use your skills to carefully fit an SARIMA model to the commodity. Later, you will use the fitted model to try and forecast the whole bird spot price.

After removing the trend, the sample ACF and PACF suggest an AR(2) model because the PACF cuts off after lag 2 and the ACF tails off. However, the ACF has a small seasonal component remaining. This can be taken care of by fitting an addition SAR(1) component.

By the way, if you are interested in analyzing other commodities from various regions, you can find many different time series at index mundi.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Plot the differenced (d = 1) data diff(chicken). Note that the trend is removed and note the seasonal behavior.
Plot the sample ACF and PACF of the differenced data to lag 60 (5 years). Notice that an AR(2) seems appropriate but there is a small but significant seasonal component remaining in the detrended data.
Fit an ARIMA(2,1,0) to the chicken data to see that there is correlation remaining in the residuals.
Fit an SARIMA(2,1,0)x(1,0,0)₁₂ and notice the model fits well.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Plot differenced chicken


# Plot P/ACF pair of differenced data to lag 60


# Fit ARIMA(2,1,0) to chicken - not so good


# Fit SARIMA(2,1,0,1,0,0,12) to chicken - that works

Edit and Run Code

This exercise is part of the course

ARIMA Models in R

IntermediateSkill Level

5.0+

Start Course for Free

You will investigate the nature of time series data and learn the basics of ARMA models that can explain the behavior of such data. You will learn the basic R commands needed to help set up raw time series data to a form that can be analyzed using ARMA models.

Exercise 1: First things first Exercise 2: Data play Exercise 3: Elements of time series Exercise 4: Stationarity and nonstationarity Exercise 5: Differencing Exercise 6: Detrending data Exercise 7: Dealing with trend and heteroscedasticity Exercise 8: Stationary time series: ARMA Exercise 9: Simulating ARMA models

You will discover the wonderful world of ARMA models and how to fit these models to time series data. You will learn how to identify a model, how to choose the correct model, and how to verify a model once you fit it to data. You will learn how to use R time series commands from the stats and astsa packages.

Exercise 1: AR and MA models Exercise 2: Fitting an AR(1) model Exercise 3: Fitting an AR(2) model Exercise 4: Fitting an MA(1) model Exercise 5: AR and MA together Exercise 6: Fitting an ARMA model Exercise 7: Identify an ARMA model Exercise 8: Model choice and residual analysis Exercise 9: Model choice - I Exercise 10: Model choice - II Exercise 11: Residual analysis - I Exercise 12: Residual analysis - II Exercise 13: ARMA get in

Now that you know how to fit ARMA models to stationary time series, you will learn about integrated ARMA (ARIMA) models for nonstationary time series. You will fit the models to real data using R time series commands from the stats and astsa packages.

Exercise 1: ARIMA - integrated ARMA Exercise 2: ARIMA - plug and play Exercise 3: Simulated ARIMA Exercise 4: Global warming Exercise 5: ARIMA diagnostics Exercise 6: Diagnostics - simulated overfitting Exercise 7: Diagnostics - global temperatures Exercise 8: Forecasting ARIMA Exercise 9: Forecasting simulated ARIMA Exercise 10: Forecasting global temperatures

You will learn how to fit and forecast seasonal time series data using seasonal ARIMA models. This is accomplished using what you learned in the previous chapters and by learning how to extend the R time series commands available in the stats and astsa packages.

Exercise 1: Pure seasonal models Exercise 2: P/ACF of pure seasonal models Exercise 3: Fit a pure seasonal model Exercise 4: Mixed seasonal models Exercise 5: Fit a mixed seasonal model Exercise 6: Data analysis - unemployment I Exercise 7: Data analysis - unemployment II Exercise 8: Data analysis - commodity prices

Current Exercise

Exercise 9: Data analysis - birth rate Exercise 10: Forecasting seasonal ARIMA Exercise 11: Forecasting monthly unemployment Exercise 12: How hard is it to forecast commodity prices?Exercise 13: Congratulations!