0
$\begingroup$

I'm trying to find out how stocks and cash react (in terms of returns) when people feel bearish/bullish and when they move asset allocation between stocks/cash.

I have three data sets: monthly Dow jones closing prices, allocation of assets between cash and stocks, and monthly proportion(%) of bullish/bearish people. Would this be a linear regression as follows:

[Dji prices]$y_1$ + [cash]$y_1$ = $\alpha$ + [bearish %]$\beta_1$ + [bullish %]$\beta_2$ + [% allocation cash]$\beta_3$ + [% allocation stocks]$\beta_4$ + $e$

I am thinking to use the t-test and the null hypothesis being that $\beta_t$ = 0 where t=1, 2, 3, and 4. Does this mean I have to do 4 separate tests to test the significance of the four variables?

Is this the right approach to do a test to find the significance of each explanatory set?

$\endgroup$
3
  • $\begingroup$ Is bearish/bullish a binary condition (where you're only ever one or the other)? Do the cash and stocks allocations add to 100%? $\endgroup$ – Glen_b Jan 26 '17 at 2:11
  • $\begingroup$ @Glen_b bearish/bullish is not a binary condition but has another "condition" called neutral, which all add up to 100%. And yes, cash and stocks allocations sum up to 100% as well. $\endgroup$ – user112947 Jan 26 '17 at 3:05
  • $\begingroup$ Then you can't identify coefficients for cash and stocks as well as an intercept, since cash + stocks is a constant $\endgroup$ – Glen_b Jan 26 '17 at 7:21
0
$\begingroup$

There is nothing wrong with doing 4 separate tests for each $\beta_i$.

As @MichaelChernick pointed out if you perform multiple hypetheses testing, the significance level for each comparison $\alpha_c$ has to be corrected to reduce type I error. Simplest correction is Bonferroni correction

$\alpha_c = \frac{\alpha}{k}$ where k - number of tests

Keep in mind that t-test is also used for one-sided hypothesis testing $\beta_j > 0$, thus you have to use $t_{1-\alpha_c/2}(n-p)$ quantile to test the hypoheses on $\alpha$ significance level.

You can also test multiple parameters at once $\beta_q = \beta_{q+1} = \dots = \beta_p = 0$ using the F-test which uses the F-Snedecor distribution

$\endgroup$
3
  • $\begingroup$ Don't you think you should do p-value adjustments for multiplicity? $\endgroup$ – Michael R. Chernick Jan 25 '17 at 20:41
  • $\begingroup$ @ŁukaszGrad Thanks. Is it correct to use [Dji prices]$y_1$ + [cash]$y_1$ as the dependent variables? I'm not sure if using the sum of the market prices and cash vectors are correct, and if I should be using market prices or returns. $\endgroup$ – user112947 Jan 25 '17 at 23:16
  • $\begingroup$ @user112947 If i understand correctly, currently you simply estimate the sum (Dji prices + cash). If you want to estimate them separately, i.e. to have [Dji]y1 + [cash]y2 = XB + e , you can use multivariate linear regression. But then B is a matrix and you should use other tests (like likelihood ratio chi-squared test). Also since [alloc stock] + [alloc cash] = 1 you should drop one of them $\endgroup$ – Łukasz Grad Jan 26 '17 at 8:40

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.