INSTRUCTION:
This course project aims to build the ARMA model for the time series of the foreign exchange between the US dollar and the British pound and evaluate the forecasting performance of the model. The econometric analysis should be implemented by the statistical software R and its integrated development environment (IDE), R studio.
The project report should be written in the style of an academic article, including abstract, introduction, econometric analysis, conclusion, and references (in Harvard style1). For the econometric tasks, you need to report the econometric results from R, and, more importantly, provide the technical description on the methods and the interpretation/discussion on the econometric results.
For example, you should include the following content for the task of ADF test:
• technical description of ADF test;
• how to choose the setting of ADF test (whether you want to allow drift and/or trend; how to select lags);
• R code to conduct the analysis;
• R output (Important: the results should be presented in nicely formatted tables, rather than the raw screenshot from R studio);
• interpretation and discussions on the results.
DATA:
The file “EXUSUK.xls” contains the monthly exchange data from Jan 1971 to Feb 2020, in total 590 observations. The data was obtained from the Federal Reserve Bank of St. Louis (https://fred.stlouisfed.org/series/EXUSUK). The data webpage also provides more information on the time series. Denote the original exchange rate as ππ‘, and the variables that we are interested are the logarithm of the exchange rate log(Yt) and its growth rate Δ log(Yt) = log(Yt) − log (Yt−1). Important: note that you will lose the observation in Jan 1971 when you calculate Δ log(Yt), and you need to delete the observation of log(Yt) in Jan 1971 accordingly.
ECONOMETRIC TASKS:
Before carrying out the following tasks, firstly split the dataset into in-sample period and out-of-sample period. The in-sample period is from Feb 1971 to Dec 2012, and the out-of-sample period is from Jan 2013 to Feb 2020. Important: you should use the data in the in-sample period2 to perform Tasks a–d and then make forecasting for the out-of-sample period in Tasks e–f.
1 https://libguides.reading.ac.uk/citing-references/referencingstyles
2 To be clear, use data between Feb 1971 and Dec 2012 to conduct Tasks a-d.
Task a. [Pre- analysis] Provide the data visualisations (time series plot, box plot, histogram, and ACF plot) and the descriptive statistics of log (Yt) and Δlog (Yt). What can you spot from various plots? What is the meaning of the descriptive statistics?
Task b. [Unit root/stationarity tests] Perform ADF test, PP test, and KPSS test on log (Yt) and Δlog (Yt). You can use AIC to select the best lag length for the ADF test and use “short” lag length for the PP and KPSS test.
Task c. [Model selection] Select the best ARMA(π, π) model for Δlog (Yt) by AIC. Please set the maximum orders as 5, i.e. π, π ≤ 5.
Task d. [Model diagnostics] Perform model diagnostics for the residuals from the best selected model. To be specific, carry out the time series plot, ACF plot, and Ljung- Box test on the residuals. For the Ljung-Box test, please set the lag lengths as 20, 30, and 50. Comment on the results of the model diagnostics.
Task e. [Forecasting] Choose the best model based on the data in the in-sample period and make forecasting for the out-of- sample period. Plot the predicted values from the best model versus the true values. Calculate the forecasting performance (MSE, MAE, MAPE, and %correct sign) of the best model.
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