unconditional mean of a trailing sample (in this case of size 200 observations), (ii) ARMA, (iii) Vector Autoregressive

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Unconditional Mean Of A Trailing Sample In This Case Of Size 200 Observations Ii Arma Iii Vector Autoregressive 1 (280.51 KiB) Viewed 14 times

unconditional mean of a trailing sample (in this case of size 200 observations), (ii) ARMA, (iii) Vector Autoregressive (VAR) model. The variable Indirect (DS) property return is defined as the growth rate of the monthly price index of the real estate stocks. The three-dimensional VAR model includes Indirect (DS) property returns and two additional monthly series: • Term spread, measured as the difference between the yields on a 20-year govern- ment bond and the three-month Treasury bill rate. • GEYR (Gilt- Equity Yield Ratio), calculated by taking the ratio of the yield on 20-year government bonds and the dividend yield on the FTSE 100. Summary statistics are reported in Table 1. 3.1. To check whether the VAR specification is sensible, a Granger-causality test is performed. A VAR(4) has been selected by the Akaike's information criterion. The results are reported in Table 2. Consider the causality from GEYR to the Indirect (DS) property returns. State the null and the alternative hypotheses of the test and comment on the outcome of the test. [15%] 3.2. The forecasts are constructed as follows. The specifications of the ARMA and VAR models have been selected by different information criteria. The sample is split roughly in half, with the first 200 observations being used for in-sample model estimation. Then a series of out of sample forecasts up to six steps ahead are generated. The sample is then rolled forward by one observation, the models re-estimated, and a new series of forecasts constructed. The procedure is repeated obtaining 160 forecasts. Table 3 reports the results for 1- and 6-month forecast horizons. Do the VAR models produce superior forecasts compared with the simplest mod- els? Did you expect it to be the case? Justify your answers. [10%] 3.3. Consider again Table 3. Would you say that more heavily parametrized model provide better forecasts? Justify your answer. [10%] 3.4. Forecasts are further assessed against the profitability of two trading rules: first, invest in the property stock index if the property return during the next period is forecast to be positive; second, invest only if the return forecast for the next month is 0.87% greater than the average return over the sample period. If the
forecast rule signals a buy, the property index is purchased. Then, the sample is rolled forward by one observation, and if the next return is predicted positive again, the index continues to be held, and so on. However, if the return is then predicted to be negative, the index is sold, with the proceeds invested in risk-free assets, like treasury bills. It is assumed that the investment began at the start of our out-of-sample period and continued for the full 160 observations (i.e. a 13 years and 4 month period). Table 4 presents the trading profitability results, denominated in simple annualized percentage returns. The "buy and hold equities/treasury bill" (bottom of the table) are the profits of an investor that either takes a long position in the equity- based property index or has no position, with the funds being held in treasury bills. A market is said to be inefficient with respect to a particular information set if it is possible to make abnormal profits from trading on the basis of that infor- mation set. Interpreting the results one should also consider the transaction cost estimated to be 1.7% of the value of the purchase/sale per transaction. Thirty trades over the forecast period can be approximated as 2 trades per year. Would you say that the results in Table 4 provide evidence of the market inefficiency? Justify your answer. [15%]