0
$\begingroup$

I'm analysing returns of funds and i have data on the following for 1000 funds.

  • Returns in Period t
  • Returns in Period t-1

I want to use a time series model to see how much returns have increased from period 1 to 2(b_1 in the following model). The model i had in mind is the following: $$ y_t = b_0 + b_1(x_t) + e_t $$ Where $y_t$ is the returns in period $t$, and $x_t$ is the returns in period $t-1$.

I've been researching time series models lately and I found that if you have data like I do I need to find the:

Autoregressive order

Integrated order

Moving Average order

But can't I just see directly that my model is a AR(1) model? Since I'm only using 1 lagged variable? Or do i have to look at graphs to determine the orders?

Thank you

$\endgroup$
  • $\begingroup$ If you know that that is your true model, then your AR order is 1, your Integrated order is 0 (you don't difference returns), and your moving average order is 0. You don't have to perform model seletion if you already have a very good idea what your model is. And yes, in this case you can use least-squared/regression to fit this model, estimating $b_0$, $b_1$ and the variance of your error. $\endgroup$ – Taylor Apr 26 '17 at 17:02
  • $\begingroup$ @Taylor Thank you for your answer. Well, since i only have data on return in period t and t+1 for each fund. Doesn't that mean that it is a AR(1) Model? Or can it be a ARMA or ARIMA model aswell? $\endgroup$ – user358065 Apr 26 '17 at 17:06
  • $\begingroup$ So your saying i could use a simple linear regression to estimate b_1? Will it not be unbiased since y_t and x_t is highly correlated? $\endgroup$ – user358065 Apr 26 '17 at 17:12
  • $\begingroup$ @Taylor So your saying i could use a simple linear regression to estimate b_1? Will it not be unbiased since y_t and x_t is highly correlated? $\endgroup$ – user358065 Apr 26 '17 at 18:48
  • $\begingroup$ An AR(1) is an ARMA(1,0) is an ARIMA(1,0,0) is the regression you wrote down. Your estimate for $b_1$ will not be unbiased. And it is precisely because $y_t$ and $x_t$ are correlated that $b_0 \neq 0$. $\endgroup$ – Taylor Apr 26 '17 at 19:07
0
$\begingroup$

The most commonly used technique to evaluate the parameters $p,q$ for $ARMA(p,q)$ models is unfortunately a brute-search over the parameter space. However, there is an objective score that a lot of people use to automatically select the optimal parameters.

This criterion is commonly called the AIC, Akaike Information Criterion, and is basically representing a trade-off between number of parameters in the model, and log-likelihood (how well the model fits the data).

The formal definition is $$AIC(k)=2k-2ln(\hat{L})$$ where $\hat{L}$ is the maximum likelihood estimate given the model with $k$ parameters.

source: https://en.wikipedia.org/wiki/Akaike_information_criterion

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.