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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 $$h_(x) = \sum_0^n \theta_i x_i = ... 4 There is a lot of ways to understand why stationarity allows to apply usual time series analysis. Here is one more. Very often, the theoretical justification of what you do in time series need to be able to identify the mean formula and the expectation:$$\frac{1}{N}\sum_{n=1}^N X_n \underset{N\rightarrow +\infty}{\longrightarrow} \mathbb{E} X, $$where the ... 3 Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility ... 2 In the case of application in finance, usually, GARCH is used in estimating realized volatility of returns based on the weight we would like to give to each past observation. Ultimately after estimating (calibrating) the parameters of the model to an existing time-series, GARCH is used for forecasting multi-step ahead return (future) volatility. Different ... 2 I am not sure to understand your question. But as far as I understand it. If you have a dataset with Y,K,L,M over a set of corporates over some years, you can estimate A using a log-log regression, since the following model is compatible with your Coob-Douglas specification:$$\log Y=a \log K + b \log L + c \log M + \log A.$$It is clearly the ... 2 I am a professor too and I did work with Siemens Corporate Technology which provides the quantitative technology for their copper and electricity trading (Siemens being one of the biggest players in this area in Europe). They are mainly using sophisticated neural networks. We also published a paper together, see my answer here: What types of neural networks ... 2 Consider the following AR(1) process with i.i.d. normal errors that have zero mean and finite variance \sigma^2>0,$$ x_t = (1-\rho)\mu + \rho x_{t-1} + \epsilon _t$$Now suppose  \rho = 1/2 and \mu = 1. This process does not have a unit root, and it is not mean stationary. At any point in time, the process has finite variance, although as time ... 2 1) Spurious autocorrelation of non-synchronous trading data was analyzed in this article: http://www.amazon.com/An-econometric-analysis-nonsynchronous-trading/dp/1245789457 During some time intervals a lot of trades occur and during some nothing happens(so prices are stale). So serial correlation of traded prices may be present but this may be due to stale ... 1 Write the series in the answer as (x_t - \mu) = \rho (x_{t-1} - \mu) + \varepsilon_t then if \rho=.5 and \varepsilon_t is N(0,\sigma^2), (x_t - \mu) is stationary with mean 0 and variance \frac{\sigma^2}{1-\rho}. A time series process can have a deterministic part and a pure random part. The definition of stationarity (strict or strong or ... 1 For Engle-Granger, I can see that you are returned a vector of 2 elements for each of the output arguments, hence you run two tests there. For the sake of clarity and the education of people interested in the post, we can say that: Since your hValues are both zero, we can say that there is a failure to reject the Null Hypothesis, which in this case is ... 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 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$$Your sampling formula from above remains still valid though, just with ... 1 Concidering 22 days of trading per month you have approximatly 132 days of trading. I highly doubt that this will be sufficient for any forecasting. The sample might be too small. Have a look here: http://research.stlouisfed.org/wp/2012/2012-008.pdf Erdemlioglu, Laurent and Neely used the data of ~10 years to conduct their survey. 1 Well, given that either LM or BHHH is supposed to stop when the Kuhn-Tucker condition is satisfied, I infer it has to be stepwise. I would say otherwise if, say, they were potentially using something like SALO (simulated annealing with local optimization), where one algorithm could profitably run in full as a sub-step of the other. 1 Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict. The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to ... 1 I would say that you can use Johansens methods to test for rank of co-integration matrix. There are tests for that. If there is no co-integration vector present and both series are I(0) then there is no co-integration. Series still might have some short-run dynamics. If series are I(1) and no con-integration vector is present then modeling these series by ... 1 In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be$$ RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t)  where RV(t,T) is an estimate of the realized volatility from t to ...