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It doesn't seem like your problem is related to the time series nature of the problem. It seems like your problem is that you have "too many" possible independent variables, and the "kitchen sink" approach of regressing on all of them is creating multi-colinearity or very low predictive ability, say as measured by $r^2$. What you should do instead is use a ...


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If you pick pl=2 and pu = 4 and your data is daily, then indeed you filter out the trend that has frequency up to 4 days. So, your trend line is a sum of trigonometric functions with the aforementioned periodicity. The cycle comprises all the other remaining frequences.


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What you are trying to do here is estimate the demand curve of a firm. Broadly speaking, even if you got data on price and quantity, you would not be able to estimate this because your right-hand-side variable (quantity) is also determined by the supply curve. This is what people call the 'simultaneity' form of the problem of endogeneity. The way to ...


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If we have a model MA(1): $y_t=\epsilon_t-\frac{1}{2}\epsilon_{t-1}$ where $\epsilon_t\sim (0,\sigma^2)$ and $\forall_{t}E(\epsilon_t)=0$ then $\forall_{l\geq 1}E(y_{T+l})=0$. The best choice of C is 0.


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Note that $u_i$ is a random residue. In the linear regression model, we assume the independence of the random residue (error term). We have two slides above for case i.i.d.: $\epsilon_i \sim (0,\sigma^2)$, thus $\forall_{i\neq j}E[\epsilon_i\epsilon_j|X]=0$ and $E[\epsilon_i\epsilon_i|X]=\sigma^2$. Later (slide 10) we assume i.n.i.d. and $\forall_{g\neq g'}E[...


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