Compute the mean square error (MSE) and mean absolute percentage error (MAPE) for all the three forecasting methods and comment on the accuracy of your forecasts.

INDIVIDUAL ASSIGNMENT I: TIME SERIES ANALYSIS AND FORECASTING

1. The assignment must be word-processed.
2. The whole assignment must be no more than 1000 words in length including any, GRAPHICS BUT NOT REFERENCES. The word count must be stated on the front page of the assignment.
3. The assessment criteria detailed overleaf will be used to mark your assignment. Please bear the criteria in mind when preparing your assignment.

MAIN PURPOSE

The purpose of this assignment is to make students familiar with some with the basics of time series analysis and forecasting.

SCENARIO

You are a Junior Stock Analyst for F&H Investment Plc, with responsibility for tracking FTSE 100 stocks on the London Stock Exchange. One of your core duties is to determine the right price and return of stocks, which in turn, informs traders on buying or selling decisions of the stocks in their portfolio.

The asset returns/pricing model used is the capital asset pricing model (CAPM), which proposes the market (systematic) risk as the single determinant of stock value.

The CAPM is estimated using the following empirical mode

)                                                                                   (1)

where, i= 1,…, N and t=1,…,T

= return on asset i at time t (your selected stock, e.g., Barclays)

= return on the risk-free asset at time t (UK govt three (3) months Treasury bill price)

= return on the market portfolio at time t (FTSE 100 Index)

and  are the coefficients to be estimated.

Your task for the month is to produce a report detailing the time series pattern, return analysis and forecast of a stock that is a constituent of the FTSE 100 index (refer to list of FTSE 100 firms). The main body of your report should be structured based on the following sections.

Time Series Analysis

Stock Returns Analysis

Forecasting

Below are detailed requirements for each component of your report.

PART ONE: TIME SERIES ANALYSIS

1. Produce a time-series graph of the monthly price series for (i) the selected stocks, (ii) the risk-free asset and (iii) the market portfolio for the past 15 years.
2. Provide a description of the patterns observed for your series plots, that is, whether you observe a trend, season, cycle, structural break, random walk or a combination of them).
3. Identify an economic/fundamental reason for the patterns observed in each of the series analysed above.

PART TWO: STOCK RETURNS ANALYSIS

1. Estimate a monthly return series for your chosen stock (), the risk-free asset (), the market portfolio.

Due to the desirable properties of logarithm transformation, the following log-return formula is to be used for calculating the return series:

where, R_t is the return on asset i at time t,  is the price of the asset at time t,  the price of asset at time t-1, ln is the natural logarithm and  is the return on stock i.

1. Plot a time-series graph of all the return series estimated and comment on how their pattern differ from that of the price series in part one.
2. Estimate a static linear regression of the monthly return series using equation (1).
3. Interpret the coefficients of your regression and comment on their statistical significance.
4. Comment on how the presence of autocorrelation is likely to affect your analysis of the result above.

PART THREE: FORECASTING

You are expected to provide forecasts of your chosen stock. These forecasts will inform the trading division on their buy and sell decisions.

1. Produce a forecast of the monthly price and return series of your chosen stock for the last 3 years using (i) the moving average method, (ii) exponential smoothing method and (iii) the regression estimates from your previous section.
2. Compute the mean square error (MSE) and mean absolute percentage error (MAPE) for all the three forecasting methods and comment on the accuracy of your forecasts.

FORMAT OF REPORT

Executive summary, introduction, logical structure, clear explanation and appropriate referencing.

WRITTEN REPORT FORMAT

The written report should be 1,000 words (plus or minus 10%) in length (including, introduction, main report and conclusion, but not the reference list), word-processed and should be of a professional format suitable for the audience.

ASSESSMENT AND MARKING SCHEME

The majority of the marks will be given to students that produce evidence of:

• A good understanding of time series analysis.
• A good understanding of time series regression analysis and forecasting.
• Critical thinking in the interpretation of the findings.

EXECUTIVE SUMMARY

An executive summary should be no more than 10% of the final word count. This is not part of the word count.