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48

You are conflating the features of a process with its representation. Consider the (return) process $(Y_t)_{t=0}^\infty$. An ARMA(p,q) model specifies the conditional mean of the process as $$ \begin{align} \mathbb{E}(Y_t \mid \mathcal{I}_t) &= \alpha_0 + \sum_{j=1}^p \alpha_j Y_{t-j}+ \sum_{k=1}^q \beta_k\epsilon_{t-k}\\ \end{align} $$ Here, $\...


25

Some points to start with: i) these distributional conventions are at best approximations. They can be convenient models, but we shouldn't confuse that with the actual distribution of stock prices or returns. ii) stock prices are typically increasing (but in any case, have changing mean; the mean isn't stable). So when we're talking about the distribution ...


18

Cochrane (p. 435, 2005) gives a simple explanation between the difference of looking at expected returns in the time series and in the cross section: Time series: How average returns change over time. Cross section: How average returns change across different stock or portfolios. So intuitively, if you study the cross section of stock returns, you want to ...


17

As babelproofreader mentioned, those that have a successful algorithm tend to be very secretive about it. Thus it's unlikely that any widely available algorithm is going to be very useful out of the box unless you are doing something clever with it (at which point it sort of stops being widely available since you are adding to it). That said, learning ...


16

Edit: I realized the answer was lacking and have thus provided a more precise answer (see below -- or maybe above). I have edited this one for factual mistakes and am leaving it for the record. Different focus parameters: ARMA is a model for the realizations of a stochastic process imposing a specific structure of the conditional mean of the process. GARCH ...


16

My first observation is that you did not lag the inputs relative to the closing price and that is why you observed such good fit. The SMA (simple moving average) uses the closing price in its calculation and the high low range encompasses the closing price, so using them to predict the closing price imparts a look ahead bias. My opinion is that if you are ...


12

I think for your purposes, you should pick a machine learning algorithm you find interesting and try it. Regarding Efficient Market Theory, the markets are not efficient, in any time scale. Also, some people (both in academia and real-life quants) are motivated by the intellectual challenge, not just to get-rich-quick, and they do publish interesting ...


11

Copying from the abstract of Engle's original paper: "These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance". Continuing with the references, as the author who introduced GARCH ...


10

To my mind, any run-of-the-mill strong AI that could do all of the following might easily produce a statistically significant prediction: Gather and understand rumours Access and interpret all government knowledge Do so in every relevant country Make relevant predictions about: Weather conditions Terrorist activity Thoughts and feelings of individuals ...


10

ARMA Consider $y_t$ that follows an ARMA($p,q$) process. Suppose for simplicity it has zero mean and constant variance. Conditionally on information $I_{t-1}$, $y_t$ can be partitioned into a known (predetermined) part $\mu_t$ (which is the conditional mean of $y_t$ given $I_{t-1}$) and a random part $u_t$: \begin{aligned} y_t &= \mu_t + u_t; \\ \mu_t ...


9

The formula for adjusted R square allows it to be negative. It is intended to approximate the actual percentage variance explained. So if the actual R square is close to zero the adjusted R square can be slightly negative. Just think of it as an estimate of zero.


8

Past volatility in the price of something is a measure of the inability of the past to predict the present, as otherwise prices would largely change smoothly just reflecting time costs, and so in many (but not all) cases it could be an indicator of how difficult it might be for the present to predict the future. Hence it becomes an indicator of risk, and ...


8

You have misunderstood (I think it's pretty clearly explained at your link). Each row gives a set of weights, across the first six columns. Those do indeed sum to 1. Note that some weights are negative. The collection of rows defines the frontier.


7

If you define the proportional return as $\Delta P/P = (P_{t+1}-P_t)/P_t$, where $P$ is the price, it's not uncommon with daily returns to simply multiply the proportional return by $250$ (number of working days in a year) and the standard deviation by $\sqrt{250}$ to annualize them. This corresponds to your case C. The point here is to rescale so that a ...


6

If you are new to the scoring world, your first book should be by naeem siddiqi on credit scoring using SAS. If you have not taken the class go for it. The class main focus is the overall understanding of scoring and selling SAS enterprise miner for millions of dollars. If you need theory you need a categorical data analysis and Data mining class from a ...


6

I work in the credit scoring field. Even though I like exploring different approaches I find that logistic regression is often good enough if not the best approach. I have not surveyed the most recent papers on the topic but from memory in most papers you will see that other approaches such as neural nets model typically do not offer significant lift in ...


6

Yes the the series should be stationary. GARCH models are actually white noise processes with not trivial dependence structure. Classical GARCH(1,1) model is defined as $$r_t=\sigma_t\varepsilon_t,$$ with $$\sigma_t^2=\alpha_0+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2,$$ where $\varepsilon_t$ are independent standard normal variables with unit ...


6

The closest you'll get is probably one of Ruey S. Tsay's books; for example, Analysis of Financial Time Series. This books covers ARIMA models in Chapter 2 and then goes on to discuss other, arguably more appropriate, models for modelling financial time-series. As noted in the comments by the reference to the work of Eugene Fama, predicting stock prices is ...


5

At heart, geometric means are what you want to work with because what you get back from investment is multiplicative - if you invest $1$ for two periods, getting $(1+r_1)$ and $(1+r_2)$ you end up with the product of the two single period amounts, $(1+r_1)(1+r_2)$ (since $(1+r_1)$ is available to invest after 1 period). The arithmetic mean would be what ...


5

As mentioned in the comments, the model you're looking for is Bayesian linear regression. And since we can use BLR to calculate the posterior predictive distribution $p(r_t|t, \mathcal{D}_\text{ref})$ for any time $t$, we can numerically evaluate the distribution $p(\text{CAR}|\mathcal{D}_\text{event}, \mathcal{D}_\text{ref})$. The thing is, I don't think a ...


5

I have never worked with recurrent networks, but from what I know, in practice, some RNN and TDNN can be used for the same purpose that you want: Predict time series values. However, they work different. It is possible with TDNN: Predict process' values Find a relationship between two processes. Some RNN, like NARX also allow you to do that, and it is ...


5

As Stephen mentions, the confusion is between: (1) the CAPM vs. (2) the market model. Let $R^f$ denote the risk free rate. We often work with excess returns, which involves subtracting of the risk free rate. Some simple models for expected returns ``Market model" $$ R_t - R^f = \alpha + \beta\left(R^m_t - R^f \right) + \epsilon_t $$ $$ E\left[ R_t \right] ...


5

They are not really different approaches in that they are solutions to different problems: one computes the sequence of filtering distributions $p(\beta_t|Y_{1:t})$, and the other the distributions based on all observations $p(\beta_t|Y_{1:T})$, for $t =1,...,T$. The smoother doesn't "hide underlying dynamics" but rather adjusts its state estimate (with ...


4

You could try the auto.arima and ets functions in R. You might also have some success with the rugarch package, but there's no existing functions for automated parameters selection. Maybe you could get parameters for the mean model from auto.arima, then pass them to rugarch and add garch(1,1)? There's all sorts of blogs out there that claim some success ...


4

The standard time series "pitfall" is the dreaded unit root or, more generally, non-stationary processes. For example, suppose price and volume are given by: $ln(price) = a + b*t +\epsilon_1 $ $ln(volume) = c + d*t +\epsilon_2 $ Running a regression will give you an exceptionally good fit (in terms of $R^2$ and t-values), but is fundamentally a ...


4

Nothing will be able to prove it one way or another, because even if you find revenue has dropped from that time, you will not be able to dismiss the possibility of other structural change (eg new competitor, changed regulatory environment, changed fashion, something you can't even think of...). You can use time series techniques to identify if the timing ...


4

If all your predictors $(X_1, \dots, X_4)$ are zero centered then the constant term is what accounts for the class imbalance. For example, if your sample has 100 1s and 400 0s then the overall background proportion of 1s is 20%, and alpha will be such that $g(0.2) = \alpha$. If you are using logit link function then $logit(0.2) = \alpha = -1.386$. The ...


4

e.g. if I start with 100 $ and if my stock then goes up +10%, and then from 110 it goes down -10%, the mean of the return would be 0, This is not necessarily about arithmetic or geometric mean. This is also about simple or continuous return. Consider this: $100(1+0.1)(1-0.1)=100(1-0.01)=99$ $100 e^{0.1}e^{-0.1}=100$ In the first case I assumed that ...


4

$\hat{L}$ is the likelihood: it's a number that comes from a Maximum Likelihood Estimation (MLE), which estimates the value of your model's parameters. The Likelihood $L(\theta | X)$ says how likely the parameter values in vector $\theta$ fit the data in $X$. It is derived from the Bayes theorem: $$L(\theta | X) P(X) = P(\theta) P(X | \theta) \quad \...


4

Later edit: I give what seems to be a better solution here. Note that the paper uses a different parameterization from the form given in the question. As Yves noted in comments, it uses $-a$ in place of your $a$ (both are common parameterizations; the only difficulty may be when it is unclear which parameterization is being used). If you convert answers ...


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