can be correlated for different stocks. This might follow from the single-index model, which is a basic model of price dynamics in financial markets. It assumes that the returns C(t) of all stocks are controlled by one factor, usually called the «market». In this model, for any stock k we have
C_k(t) = alpha_k + beta_k * M(t) + eps_k(t) (1)
where C_k(t) and M(t) are the return of the stock k and of the «market» (e.g. RTS index), alpha_k and beta_k are constants for a given stock (during some relatively large time interval), and eps(t) is a zero mean noise term. The noise terms of different stocks are assumed to be uncorrelated. The covariance between M(t) and eps_k(t) is set to zero for any k.
Now, if we assume that the hyposysis (1) is true, we get some constraints on your model:
C_k(t) = a_k(i) + b_k(i)*t + N(t) for t(i-1) (<) t (<)= t(i) (2)
For example, b_k(i) must be strongly correlated for different stocks:
for any k,s: b_k(i)/b_s(i) = const (not depending on i). Did you observe such correlations?
Moreover, the trendfollowing model, based on (1), can be more convenient if one deals with the portfolio of stocks: one can model the trend only for the market as far as alpha_k and beta_k are stable during the considered period. What do you think about that?
