# Tag Info

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I can only talk about quantitative trading. As a rule of thumb, the lower frequency you work in, the more econometrics is important, whereas for a higher frequency, the more econometrics becomes useless. (I would still recommend a top econometrician for HFT since they have what it takes to succeed, it's just the models aren't out-of-the-box applicable.) But ...

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It's an interesting question. I particularly agree with the $\mathbb{Q}-\mathbb{P}$ dichotomy mentioned by many. I would add to the other answers that, come to think of it, the Black-Scholes postulated Geometric Brownian Motion could be interpreted as an AR(1) process on the logarithm of the stock price as you discretise the SDE from which it is a solution,...

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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 you need to differentiate between Q-quants vs P-quants. The former might not use Econometrics, but P-quants use them a lot.

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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 $$r_{2,t} \sim N\left(0,\sigma_{2,t}^{2}\right)$$ $$\sigma_{2,t}^{2} = \beta_{... 11 Traditional econometric (time series) models are of little or no value in forecasting market prices for purposes of "making money", i.e, generating excess return over a benchmark in an asset management setting. They have some limited value in strategic and tactical asset allocation. The ineffectiveness of time-series modeling in asset management stems ... 9 Treat the estimate of standard deviation as a random variable. Then you can bootstap the sample estimate and generate t-statistics and associated confidence intervals for your statistics. I describe a generic boostrap process on this post. 9 GARCH will work if volume has memory with some decay. AR will work if volume has mean reversion properties. Both of these are empirical questions and depend on the market. You should also consider if there are seasonal (day-of-week, monthly, quarterly effects) in which case you would want to add dummy variables. MA models will work well if volume behaves ... 9 The best paper is probably Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch. In this paper the volume is modelled via a Point Process, and theoretical laws are derived (with confident intervals, etc). And we put elements about this in Market Microstructure in Practice, Chap 2.1. Volume curves are analyzed, not only during the ... 9 Define excess return r^x_{it} = r_{it} - r^f_{t} as the return i minus the risk free rate, and f_{jt} similarly denotes the excess return of factor j at time t. Let's say we have some factor model of returns where:$$ r^x_{it} = \alpha_i + \sum_j \beta_{i,j} f_{jt} + \epsilon_{it}$$F-test / GRS Test If we assume the error terms \epsilon_{it} ... 8 Glad you've asked :) Technically speaking, in factor model \alpha stays for return or risk premia, which asset pays when all factor returns are zero. Then, to answer question in more details, we have to specify, are we dealing in our model with return (R_i for asset i) or with risk premia over risk free (R_i-R_f). In the first case, ... 8 The bias comes from the paper Stambaugh (1999) and has nothing to do with small sample bias. It has to do with point (1) below. The argument goes as follows: Typical lagged explanatory variables for stock-return regressions are correlated with contemporaneous stock returns This contemporaneous correlation biases forecasting regressions First review OLS ... 7 There is a lot of ways to understand why stationarity allows to apply usual time series analysis. Here is one more. Very often, the theoretical justification of what you do in time series need to be able to identify the mean formula and the expectation:$$\frac{1}{N}\sum_{n=1}^N X_n \underset{N\rightarrow +\infty}{\longrightarrow} \mathbb{E} X, $$where the ... 7 @user2763361 has a very thorough list of useful econometric topics for quantitative finance. I would add missing, mixed frequency, and irregular data as major issues that I'm either constantly dealing with or begrudgingly ignoring. Seasonal adjustment is important too for some data (like electricity futures), though the subject is also related to his ... 7 Having thought about this I think the following reason is also important and wasn't mentioned so far: When you look at the inner working of this whole class of econometric models it all boils down to the following: It is possible (under some reasonable assumptions) to express any MA(q) model as an AR(\infty) model (and vice-versa for expressing AR(p) ... 7 Without seeing your trading desk's P&L it's impossible to say whether it is predictable or not. But here are a few thoughts - There's no reason to think that it isn't predictable. In general, financial time series are hardest to predict when the represent the return stream of an investible asset. A trading desk's P&L isn't really investible, so ... 6 I basically agree with @John, let me expand: We want to model y using a simple linear model, the most basic setup is$$ 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. ... 6 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 ... 6 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 ... 6 My answer is very much in the spirit of Kiwiakos' answer. E.g. in this paper (where I am one of the coauthors) we use VMA (vector moving average) models (in the multivariate case) and AR models in the univariate case to calculate proper scaling of volatility or its contributions if there are (cross-) auto-correlations. This happens in the P world due to ... 6 Financial economics is what economics calls finance. Finance is what finance calls finance. Less flippantly though, there's a long debate on whether finance is a subfield of economics, and this debate goes back at least to the PhD thesis of Markowitz. Prof. Milton Friedman famously opposed awarding Markowitz a PhD in economics from the University of Chicago ... 5 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 "... 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} \big(\overline{X}_n-E(... 5 No, a sum of two GARCH processes is generally not a GARCH process. (I am not even sure whether there exists a nontrivial special case where the opposite holds.) By GARCH I mean the classic definition of GARCH due to Bollerslev (1986), not an arbitrary variation like EGARCH, IGARCH, FIGARCH or whatever else. Let me provide an example. Take two ... 5 An AR(1), once the time series and lags are aligned and everything is set-up, is in fact a standard regression problem. Let's look, for simplicity sake, at a "standard" regression problem. I will try to draw some conclusions from there. Let's say we want to run a linear regression where we want to approximate y withh_(x) = \sum_0^n \theta_i x_i = \...

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The idea of skipping a month was already in Jegadeesh and Titman 1993. The key academic paper in this area. Jegadeesh himself (without Titman) discovered a 1-month return REVERSAL effect in 1990, so it makes sense that he would take out 1 month in calculating returns in his later (1993) study. He already knew what happens to stocks that are up a lot ...

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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 ...

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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.

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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, ...

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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 ...

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