Univariate Time Series Models
(M. Sc. Financial - Exercise 4)
Soberano College Organization School w. [email protected] ac. uk
Consider the following three models that a researcher advises might be reasonable models of currency markets prices. yt yt yt = ytв€’1 + lace = zero. 5ytв€’1 & ut = 0. 8ytв€’1 + lace
(a) What classes of models happen to be these examples of? (b) What would the autocorrelation function for each of those processes appear to be? (not exactly, just the shape) (c) Which model is more likely to represent stock market prices coming from a theoretical perspective, and why? In the event that any of the 3 models really represented the way stock market rates move, that could potentially be taken to make money? (d) Consider the magnitude of determination of shocks in the series in each case.
You get the following quotes for an AR(2) model of some returns data. yt = zero. 803ytв€’1 + 0. 682ytв€’2 + ut, where ut is a white-noise error procedure. By evaluating the characteristic equation, examine the estimated version for stationarity.
Question a few
A researcher is trying to look for the appropriate order of an ARMA model to spell out some data, with 2 hundred observations readily available. She has the next п¬Ѓgures for the log of believed residual variance (log(Л† a couple of )) for various prospect models. This lady has Пѓ thought that an buy greater than (3, 3) should not be necessary to unit the mechanics of the info. What is the " optimalвЂќ model order? ARMA(p, q) model purchase log(Л† a couple of ) Пѓ (0, 0) 0. 932 (1, 0) 0. 864 (0, 1) 0. 902 (1, 1) 0. 836 (2, 1) 0. 801 (1, 2) 0. 821 (2, 2) 0. 789 (3, 2) 0. 773 (2, 3) 0. 782 (3, 3) 0. 764
" Given that the objective of any econometric modeling exercise is to п¬Ѓnd the model that a lot of closely вЂп¬Ѓts' the data, in that case adding more lags to an ARMA model will certainly almost almost always lead to a much better п¬Ѓt. Therefore , a large style is best as it will п¬Ѓt the data even more closely. вЂќ Comment on the validity (or otherwise) of this statement.
(a) You obtain the...