Autocorrelation (part 3): Box-Pierce and Ljung-Box Q-tests (Excel) 

Hi Hayo, and thank you so much for such kind words! Thanks for the advice as well, we are planning to do as such and post links for additional materials on the topic in every video description. It might take some time, but I think we will complete updating all of our descriptions with some further reading materials as well as spreadsheet Google Drive by late August :) Hope it helps!

Hi, thanks for the comment! Glad the video helped you with your studies :)

Hi Priya and many thanks for the feedback! We have already got a video on Dickey-Fuller test and augmented Dickey-Fuller test, check it out: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-KCFLfQHZODM.html

@@NEDLeducation I am wondering if you will be adding videos explaining time - varying auto regression...

@@saipri Hi Priya, time-varying autocorrelation is a rather broad topic, there are multiple approaches to it. First, we can use some variable to hypothesise that autoregression magnitude depends on it (for example, autoregression is negative when traders are unexperienced and closer to zero when traders are experienced due to behavioural reasons). Second, we can have completely arbitrary autoregressive coefficients observation to observation and use a procedure like LASSO to arrive at optimal trade-off and avoid overfitting. We might do a video on the latter in the near future. Hope it helps!

@@NEDLeducation Sure! Appreciate your reply...

Hi Subha, and thanks for the question! For an F-test, you do have two degrees of freedom parameters, one equal to the number of explanatory variables (here 3), and another equal to the more conventional number of observations minus the number of restrictions. Hope this helps!

Hey sorry to disturb you again I didn't get you yes there are 3 explanatory variables but what is conventional number and number of restrictions that you are referring to

@@subhat6673 Hi Subha, and thanks for the follow-up question! The number of restrictions is the number of parameters which is typically one larger than the number of explanatory variables as it includes the constant.

Hi Johannes, and glad you liked the video! It is true that as the number of lags substantially increases, there is a degrees of freedom reduction and a risk of multicollinearity as well. You could select the appropriate number of lags using either an F-test or an information criterion, for example the Akaike information criterion.

Hi Ando, and many thanks for the excellent question! While autocorrelation coefficients are very similar to autoregressive terms from the Ljung-Box test, these need to be estimated simultaneously, so I do not feel the analogy is correct unfortunately.

@@NEDLeducation Thanks for your answer. Allow me to ask a follow-up question. I constructed an AR11 model with the LINEST function to get 11 autoregressive terms, and I also calculated the first 11 autocorrelations from a time series of stock returns. I did this to scale monthly Sigma to annual Sigma following [Lo, 2002]. However, when looking at both, I was confused: The AR11 terms are substantially different from the 11 (independently) calculated autocorrelation coefficients. In particular, my AR11 Lag 1 coefficient is something like -0.11 while the Lag 1 autocorrelation coefficient that I calculated from stock returns directly is only -0.0285. Moreover, the AR11 terms plugged into Q-Statistic indicate that the returns have statistically significant autocorrelations while my directly computed autocorrelation coefficients (when plugged violently into Q-Test lol) are not statistically significant. On a similar note, an additional AR3 model I constructed gives terms that are quite similar to my direct calculations of the Lag 1-3 autocorrelation coefficients, differ substantially from the first 3 AR11 terms, and are not statistically significant. Now, given that both coefficients differ substantially, I am wondering which one is actually a correct estimation of the autocorrelation. What would be your take on this? I am very new to the whole topic so maybe I am missing something obvious.

Hi Mot, thanks for your request! We will record a video on Arch and Garch after we finish with heteroscedasticity series, so stay tuned!

Hi Vaibhav, cannot state with certainty as I cannot see what is going on in your spreadsheet, but I suspect the sample size is either reduced because of 1258 prices generating 1257 returns, or because you reduce the number of returns by 1 naturally when calculating the lags. Hope it helps!