# 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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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, ...

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@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 ...

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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 $y$ with $$h_(x) = \sum_0^n \theta_i x_i = ... 4 The return equation is just an econometric equation that models stock returns (or other asset returns) as a function of: (i) intercept (i.e. the average return), (ii) some independent variables/features, (iii) noise that has zero mean and time-varying variance. There are sometimes other things in the return equation too that form more advanced models. The ... 3 Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility ... 3 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 ... 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 2) Alternative to Fama-MacBeth is Fama-French approach. Explanation of difference see, for example, here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1271935 Fama-French approach was used by Carhart (introduced momentum), Pastor-Stambaugh (introduced liquidity), Fama-French themselves (used it to build 5-factor model), and many other (elsevier or ... 2 The key assumption is that there is no time-series correlation between the error terms. Fama-MacBeth can deal with cross-sectional correlations. See Samuel Thompson's "Simple formulas for standard errors that cluster by both firm and time" in the Journal of Financial Economics (2011) for a treatment of different regression methods for testing equity ... 2 From my point of view, dynamic models like the one developped in Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch to provide a dynamic forecast of the volume does not improve significantly the forecasting comparing to a static volume curve forecast using historical data (last month intraday data, and an EWMA algorithm). I've ... 2 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, $$where the ... 2 Saying that you can't analyze something as is does not make it garbage. You can't eat flour "as-is", but that doesn't mean you throw it out. In order to use "standard" analysis tools, you must first transform the series into something compatible. Some examples of such a transformation include k-th order differences or a log transformation. These ... 2 Try the following : perform the logarithmic transformation of the volume data. check if the transformed data fits the normal distribution nicely. if you are working with intraday volume, then adjust for the seasonality for time of the day effect, if using daily data, in some cases some special seasonalities like expiry day, etc might be applied but it may ... 1 What you could do is to apply the methods of portfolio risk analysis. If you buy n stocks with percentages w_i,i=1,\ldots,n then your portfolio return is r = \sum_{i=1}^n w_i r_i. Dealing with investment strategies I would not include an expected profit in the VaR calculation and put \mu=0 for this reason. To calculate the volatility of your ... 1 If the returns are N(\mu,\Sigma) distributed, then WML\sim N(0,\sigma), because the equally-weighted \mu's cancel while \Sigma=\sqrt{w \Sigma w'} with w=\{1/n...1/n\}. So your new VaR becomes:$$\mbox{VaR}\left(\alpha\right)_{WML}=\Phi^{-1}\left(\alpha\right)\cdot\sigma$$Your sampling formula from above remains still valid though, just with ... 1 Well, given that either LM or BHHH is supposed to stop when the Kuhn-Tucker condition is satisfied, I infer it has to be stepwise. I would say otherwise if, say, they were potentially using something like SALO (simulated annealing with local optimization), where one algorithm could profitably run in full as a sub-step of the other. 1 A naive reason has been explained by Nassim Nicholas Taleb in his book titled Black Swan. In a deeper look, one should be aware that no historical data analysis can truly estimate the real tail risk of financial markets. By the same token, standard deviation, max drawdown, expected shortfall, VaR, Conditional Var... No single or combination of such ... 1 Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict. The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to ... 1 I would say that you can use Johansens methods to test for rank of co-integration matrix. There are tests for that. If there is no co-integration vector present and both series are I(0) then there is no co-integration. Series still might have some short-run dynamics. If series are I(1) and no con-integration vector is present then modeling these series by ... 1 In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be$$ RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t)  where RV(t,T) is an estimate of the realized volatility from t to ...

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The classical assumptions of linear regression are that the errors are uncorrelated and the variance of errors is constant (homoskedastic). So regress the returns against the indicators and test for autocorrelation and heteroskedasticity in the errors. If you don't observe any, then there's no issue with conventional hypothesis testing. If you do, use White ...

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As an overview, Expected Returns, by Antti Ilmanen, was recommended to me. He has a preference for data over theory, so it will appeal to quants. The book is longish, and got a bit heavy at times, but he covers all the investment products and all styles of investing. The biggest problem might be that it is now 3 years old, and was heavily influenced by ...

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