# Tag Info

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You may want to first broadly categorize volatility models before comparing between them within each class, it does not make sense to compare standard deviation models with an implied vol model. I would broadly classify as follows: Historical realized volatility: Those include standard deviation (sum of squared deviations), realized range volatility ...

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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 $$r_{2,t} \sim N\left(0,\sigma_{2,t}^{2}\right)$$ $$\sigma_{2,t}^{2} = ... 8 Treat the estimate of standard deviation as a random variable. Then you can bootstap the sample estimate and generate t-statistics and associated confidence intervals for your statistics. I describe a generic boostrap process on this post. 6 GARCH will work if volume has memory with some decay. AR will work if volume has mean reversion properties. Both of these are empirical questions and depend on the market. You should also consider if there are seasonal (day-of-week, monthly, quarterly effects) in which case you would want to add dummy variables. MA models will work well if volume behaves ... 5 The best paper is probably Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch. In this paper the volume is modelled via a Point Process, and theoretical laws are derived (with confident intervals, etc). And if you can wait few days (it will be available very soon), we put elements about this in Market Microstructure in Practice, ... 5 I basically agree with @John, let me expand: We want to model y using a simple linear model, the most basic setup is$$ 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 $\beta$. ...

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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} ... 5 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 ... 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 Working on trigonometric polynomial decomposition, the first step is to take a big look at Fourier transformation. It is very powerfull, well documented and probably well implemented on your favorite language. It will give you the decomposition of your time series. You can remove highest frequencies, which correspond to noise, to have a good estimation. 3 Building upon +Imorin answer, you should have a look specifically at discrete cosine transforms. It's a standard approach when trying to express finite sequences as a sum of cosines. I would start from there, especially as it's implemented in every common language (R, Matlab, Python for starters). Only then evaluate if you need more. 3 There are tons of quant related blogs out there, some of which contain relatively sophisticated content, others less so. Have a look at the following, which aggregates blogs: MoneyScience Otherwise I could point you to bank/sell-side research. Have a look at the freely available Reuters Messenger (RM), they maintain channels where you can be permissioned ... 3 You could read it like this: The typical change in equity value is equal to the typical change in asset value, adjusted for the probability of the assets surviving. Note that the formula is not specific to Merton models, it's also true for regular options and their underlyings. It's just that volatility of option prices isn't typically a concern in ... 3 Well, the main intuition of the Merton model is that a company's equity can be treated as a call option on its assets, thus allowing for the application of Black-Scholes option pricing methods. Let's consider a company that has assets$A_{t}$financed by equity$E_{t}$and a zero-coupon debt$B_{t}$with face value K, and maturity T. At time of maturity T, ... 2 I would recommend to use simple standard deviation (among the 2 options you offered). You are performing time series analysis of historical data points, you are not forecasting. Thus, why exposing yourself to a much more computationally intensive method? May I also point you to a related (not duplicate) thread: Why are GARCH models used to forecast ... 2 What you are talking about is called regression using fractional polynomials and it has its merits. The canonical reference is this one: Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling by Royston and Altman (1994) From the abstract: The relationship between a response variable and one or more ... 2 See edit and comments, this response might not be applicable to the question: When performing regression you would tend to want your regressors to be of similar type, or at the very least range. Assuming you use log return for price changes I would recommend using the untransformed interest rate. The reason for this is that they are the same type of entity, ... 2 The equation stated in the question is not at the core of Merton's credit model, (Not saying you claimed it is) but is a simple device in helping to solve the system of linear equations. The equation given simply establishes a relationship between the volatility of equity and the volatility of the assets and it follows from the application of Black Scholes ... 2 I deal recently with some analysis of the Volume time series, daily volume in € for European stocks. I found out that an ARIMA model works well. But, some EWMA could also provide good forecast if it's well parameterized. You can also face some seasonality effect due to macroeconomic events, some you may need to clean you data and treat these days in a ... 2 In the Ljung-Box test, the null hypothesis is:$H_0$: The data are independently distributed So, your p-values of 0 indeed indicate that you should reject the null hypothesis, but it means that your data is not independently distributed, and in particular that there is some significant autocorrelation in the process. This is obviously the case, because ... 2 I have a little experience with this. First, NASDAQ has shared a dataset with researchers that flags whether an HFT participated in each trade or not but not the actual MPID - probably less granular than what you want. You generally need a professor to "cosign" your request, write a brief project proposal, and sign an NDA to get it. They also have shared ... 1 Market participant ID data is extremely unlikely to be available without the collaboration of regulators and the exchange itself, as it is a closely guarded information. Even "anonymized" data with no reference to a specific firm could reveal private information to informed market participants. If obtained at all, it is likely to come with draconian ... 1 Saying that you can't analyze something as is does not make it garbage. You can't eat flour "as-is", but that doesn't mean you throw it out. In order to use "standard" analysis tools, you must first transform the series into something compatible. Some examples of such a transformation include k-th order differences or a log transformation. These ... 1 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 can' read your lm lines but I think this works: mymodel = lm(sales~year+I(year^2)) plot(sales) lines(fitted.values(mymodel)) Or you try just mymodel = lm(sales~I(year^2)) Finally new.data = list(year=2004) predict.lm(mymodel,new.data) gives a useful value. 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 ... 1 Economically, the interest rate should be stationary. Unlike a price series, where a price of$10 may not have had the same meaning for a given stock many years ago as it does today, an interest rate of 10% always means the same thing. Hence I side with Andre's earlier answer that you should use the untransformed interest rate. Also, you need to think more ...

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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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