Dear Thom
i refer to the textbook example of Franses, van Dijk and Opschoor, "Time Series Analysis for Business and Economic Forecasting", 2nd Edition on page 92. I want to examine ARFIM models for forecasting security and commodity prices and the AML estimation method appears as easier to implement for my skill level. Adopting the example, which is for absolute values of one period log-price changes and including also an AR term or more lags in the FRML instruction epsf function is straight forward. Also estimating the fitted values for the dependent variable is not a difficult task. Unfortunately, the example code and also the text of the book, as far as i have seen on an excerpt stops here. FDO only show that the left hand side is not y, the dependent variable, but (1-L)**d(y-m). How can I compute (1-L)++d in order to isolate y on the left hand side of the equation? Is there a function available in RATS, which does the calculations for various numbers of lags L and d-parameter? Any hint would be helpful.
Best regards
PeterF
ARFIM example from Franses, van Dijk and Opschoor
Re: ARFIM example from Franses, van Dijk and Opschoor
Hello,
I have found the solution. Some textbooks describe the backshift operator only briefly, Thus, there is often the wrong expression that L or B would take certain values, for example the number of lags. But this is wrong. It is just an operator and mathematical rules apply also to this operator. Both sides of the equation have to be divided by (1-l)**d, which is equivalent to multiplying both sides with (1-L)**-d. Thus, we have left y-m = (1-L)**-d multiplied with the fitted series. Thus, once the fitted series is calculated, the instruction diff(fract=-d) start end fitted_series y-fitted will return the estimated series of the ARFIMA model. This does not only apply to the AML estimate of the textbook example from Franses, van Dijk and Opschoor, but also for the two step estimation process.
Best regards
PeterF
I have found the solution. Some textbooks describe the backshift operator only briefly, Thus, there is often the wrong expression that L or B would take certain values, for example the number of lags. But this is wrong. It is just an operator and mathematical rules apply also to this operator. Both sides of the equation have to be divided by (1-l)**d, which is equivalent to multiplying both sides with (1-L)**-d. Thus, we have left y-m = (1-L)**-d multiplied with the fitted series. Thus, once the fitted series is calculated, the instruction diff(fract=-d) start end fitted_series y-fitted will return the estimated series of the ARFIMA model. This does not only apply to the AML estimate of the textbook example from Franses, van Dijk and Opschoor, but also for the two step estimation process.
Best regards
PeterF