# Tag Info

10

I think there are a lot of different ways to specify this problem. For simplicity, consider independent Garch processes $$r_{1,t} \sim N\left(0,\sigma_{1,t}^{2}\right)$$ $$\sigma_{1,t}^{2} = \beta_{1,1}+\beta_{1,2}\varepsilon_{1,t-1}^{2}+\beta_{1,3}\sigma_{1,t-1}^{2}$$ and $$r_{2,t} \sim N\left(0,\sigma_{2,t}^{2}\right)$$ $$\sigma_{2,t}^{2} = ... 8 Treat the estimate of standard deviation as a random variable. Then you can bootstap the sample estimate and generate t-statistics and associated confidence intervals for your statistics. I describe a generic boostrap process on this post. 5 Actually you should be interested by the Berry Essen's theorem which precises the rate of convergence of the central limit theorem. Given i.i.d. X_1,\dots, X_n \sim X 1) GLN : assuming E(X)<\infty then \overline{X}_n-E(X)\to 0  2) CLT ("rate" of the GLN) : assuming E(X^2)<\infty then \frac{\sqrt{n}}{\sigma^2} ... 4 They are not mutually exclusive. For example, the class you refer to as "econometric" are simply linear regression models that include as factors prior returns or residuals of the return series sometimes with weightings on the observations. You could easily design a neural network with no hidden layers and the same inputs. So each of the econometric models ... 4 GARCH will work if volume has memory with some decay. AR will work if volume has mean reversion properties. Both of these are empirical questions and depend on the market. You should also consider if there are seasonal (day-of-week, monthly, quarterly effects) in which case you would want to add dummy variables. MA models will work well if volume behaves ... 3 From an academic viewpoint you do not have a lot of choices: The Rosenbaum-Robert approach, the price model with uncertainty zones is a model of trades and duration between trades (implicitly). It is worthwhile to try it. You can also use an Hawkes process, it will have the nice effect of capturing clustering effects on trades. if you want to use ... 2 I would recommend to use simple standard deviation (among the 2 options you offered). You are performing time series analysis of historical data points, you are not forecasting. Thus, why exposing yourself to a much more computationally intensive method? May I also point you to a related (not duplicate) thread: Why are GARCH models used to forecast ... 2 I basically agree with @John, let me expand: We want to model y using a simple linear model, the most basic setup is$$ y = c + \mathbf{X}\beta  with $y$ the $N$ observations, $c$ a constant, $\mathbf{X}$ the $N \times M$ matrix of regressors and $\beta$ a $M$-dimensional vector of coefficients. This model has $M$ parameters, the elements of $\beta$. ...

2

See edit and comments, this response might not be applicable to the question: When performing regression you would tend to want your regressors to be of similar type, or at the very least range. Assuming you use log return for price changes I would recommend using the untransformed interest rate. The reason for this is that they are the same type of entity, ...

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When you ask for "expected economic growth" you need to be specific for what you are asking for. I assume you mean GDP. But what "economic growth" is depends on who you are talking to. In my business (real estate finance, more specifically class A multifamily and industrial in 1st tier cities) economic growth has been spectacular in the past two years with ...

1

I would not call them "estimators" but rather measures because this is volatility on historical returns. The reason why there are different such measures is because each one represents volatility in different ways in order to measure the volatility of different dynamics, be it price, return, upside price moves only, down side price moves only, intraday ...

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It exists several techniques to deal with mixed-frequency data. I believe MIxed DAta Sampling is the best-known. Eg: bridge equation, MIxed DAta Sampling (MIDAS) models Mixed frequency VARs Mixed frequency factor models ... Here is a good document on this topic: A survey of econometric methods for mixed- frequency data

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Neither of the options is strictly superior over the other. I agree with Freddy about the disadvantages of GARCH. On the other hand, correcting for heteroskedasticity can help your model and forecasts* if it is present and persistent. Whether GARCH is your best choice is debatable. You could look at other sources to determine the volatility or, as an option ...

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What could be interesting would be to try and categorize what type of stocks react most to your indicators (small/large cap, country-specific). You can also see across asset classes what the reaction was. How did equities do compared to commodities or bonds or hedge funds (who are supposed to benefit from falling markets).

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