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Questions tagged [statistics]

The study of the collection, organization, analysis, and interpretation of data. Questions may deal with descriptive statistics, probability distributions, random variables, sampling, regression, density estimation, filtering, inference, estimation theory, or computational statistics.

0
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1answer
38 views

serial correlation and CUSUM results

I have the following CUSUM test resulted from autoregressive distributed lag models (ARDL). Does the CUSUM results show that the model is stable? I am a bit confused because the red line in CUSUM ...
1
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0answers
34 views

Statistical distribution of MACD

I was (unsuccessfully) trying to find results on what the distribution of the MACD values for a stationary time series with IID returns would be. Are there any such results or any that go in a similar ...
1
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0answers
29 views

Using CFNAI index for identifying sample periods

I'm doing my Thesis on Asset pricing models and I would like to find out the effects of business cycles on the performance of asset pricing models for industry portfolios. My initial idea was to ...
1
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0answers
16 views

Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
-2
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0answers
55 views

Show that the variance of the market portfolio is the weighted average of the covariance of its constituents with the market portfolio itself [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
1
vote
2answers
30 views

How to obtain annualized IR from t-monthly IC?

When we checking the relation between some factors and Stock price, we could use Information Coefficient(IC) to meausre. And then I already have t-monthly IC for each factor, and I need to calculate ...
1
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0answers
27 views

Why Jarque - Bera values are so high? Is this normal? [closed]

Please advise whether the following is a normal occurrence: In the above table I have Autocorrelation at lag1, LB, Skew, Kurt and JB test. I have noticed that whenever the value of Kurt increases, ...
1
vote
1answer
34 views

Backtesting model results, but backtesting output sampled at different frequency than model output

So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to ...
0
votes
3answers
138 views

bayes theorem probability Jar [closed]

I am trying to come up with different theoretical answers below. I believe the standard one is based on Bayes theorem, but I am struggling to prove it. A jar has 1000 coins, of which 999 are fair ...
0
votes
2answers
49 views

Annualisation of Downside Deviation

Is it possible to annualise the downside deviation? If so, on the basis of what theory? The downside deviation (DD) of a series of daily returns is computed according to the formula: $\text{DD} = \...
0
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0answers
73 views

What is 'conditional variance' in a GARCH model?

How can a single observation possess variance (by definition it is 0)? For example, we read notation such as sigma(t) as the conditional variance at time t? Yet GARCH's generate conditional variances ...
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0answers
50 views

Nonlinearity in returns?

Reading academic papers on hedge funds, I find that many authors saying that hedge fund returns are often non-linear and thus many simple quantitative techniques are not suitable. It seems like they ...
1
vote
1answer
147 views

How to calculate one-year forward one-year rate? [closed]

I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% ...
0
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0answers
22 views

Gluing the error terms to a VAR model

I am trying to simulate a VAR model with heterokskedastic errors. I have no problem simulating a VAR model, And I have no problem simulating heteroskedastic errors. My problem is trying to do ...
1
vote
1answer
44 views

Cross Product Ratio Analysis

Can you please advise? I have been recently trying to sort this out for couple of days but cannot get the same numbers as previous authors: The equation is shown in Agarwal and Naik Multi-Period ...
1
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0answers
31 views

How to count [and report] the values of significance at 1% and 5%?

I am slightly confused with this: I have calculated the Chi square for the number of funds and the methods description tells me that if the values I have calculated are greater than 3.84 (6.64) that ...
1
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0answers
35 views

Log likelihood function, GARCH(1,1) with asymmetric term

I am modelling a GARCH(1,1) and a GARCH(1,1) with an asymmetric term. $$h(t)=\omega+\alpha\varepsilon(t-1)^2+\beta\sigma(t-1)^2$$ and $$h(t)=\omega+\alpha u(t-1)^2+\beta\sigma(t-1)^2 + \gamma (u(...
1
vote
1answer
101 views

How did Dickey and Fuller know something was wrong?

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here ...
0
votes
1answer
54 views

Mean Variance optimization on hourly data with gaps

I'm building a mean variance optimizer for a portfolio of FX, commodity and bond futures. The input data is hourly returns for each underlying. Given each underlying has different market opening hours,...
-1
votes
1answer
74 views

How to calculate number of round trips given volatility?

Suppose we know stock price volatility is normally distributed with mean = 0 and annual volatility say 20%. Let's assume markets never close and we can trade at 1 second intervals. Let's assume stock ...
0
votes
2answers
56 views

Testing which index is a better benchmark to track stock prices

Let's say a Hedge Fund is tracking a stock price. Now the fund has three columns of data, Stock price, Index 1, and Index 2. All of these have data from 2016/01/01 - 2017/01/01. If the fund is to ...
2
votes
2answers
96 views

Statistical estimation vs Stochastic calibration of models

I have never been able to deduce the precise differences between model building from the statistical perspective and the stochastic processes/calibration perspective. I can only infer that these are ...
1
vote
1answer
56 views

Kalman filter state/measurement noise

In a linear Kalman filter, we assume that the state and measurement noise are white noise N(0,Q) and N(0,R) respectively. Is it common practice to test these hypothesis? And what are the most common ...
1
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0answers
21 views

Sample distribution of cross-sectional statistics of returns

Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
1
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2answers
64 views

Sample from aggregate portfolio distribution versus individual asset distributions

Suppose I have three assets $x_1,x_2,x_3$ in a portfolio with weights $W=\begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} $, expected returns $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
1
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0answers
22 views

Choosing observations/sample selection in behaviour credit scoring models

In retail banking the credit risk of a creditor after the credit had been granted is often modeled using behavioral credit scoring. In this setting the customer already has an account (or a few) and ...
0
votes
1answer
73 views

How to apply derived beta to daily change?

I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the ...
2
votes
0answers
78 views

Does Academic Research Destroy Stock Return Predictability?

McLean/Pontiff (2016) give evidence that portfolio returns are 26% lower out-of-sample and 58% lower after publishing an academic paper on variables, which are likely to predict cross-sectional ...
1
vote
1answer
73 views

selecting key performance indicators for a stock

Say, I read a financial statement of a company, and it reports, maybe 20-30 metrics, both generic, like revenue, free cash flow and specific to the company, like iphone sales etc. Is there a ...
2
votes
1answer
122 views

Why does computing correlation between index levels vs. percentage changes yield completely different results?

I am examining the relationship between the S&P 500 and the Industrial Production Index. Computing the correlation between these these variables yield vastly different results if expressed in ...
1
vote
2answers
137 views

Estimating realised gains given growth rate and churn

If one can estimate that the value of an investment portfolio will grow at $g$% per annum, and can estimate that approximately $c$% of that portfolio will be churned each year (sold and reinvested), ...
3
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0answers
88 views

Which areas of statistical physics do not get enough attention in quantitative finance?

It seems that over the past few decades many ideas from statistical physics have been successfully incorporated into economics and finance to form the sub-discipline of econophysics. However, it is ...
1
vote
1answer
101 views

Why futures pricing not calculated like options?

I have read about futures and options ( from online resources ). I only have the basic understanding,not math heavy ( for eg. for Black Scholes I know only the intuitive idea from the khan academy ...
0
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3answers
96 views

Filling a few missing data in time series?

I'm writing a paper about Uncertainty indices like VIX, etc. I already collected all data but it seems that some of the variables got a few or a little more missing data. I have daily and monthly data ...
0
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2answers
104 views

Measuring correlation between random variables when they are not normally distributed?

I want to perform some analysis on portfolio that consists of hedge funds (thus fund of hedge funds) In particular, I want to know the relationship between the funds during the downmarket. The ...
3
votes
1answer
546 views

How to have an unbiased estimation of the standard deviation when using rolling returns?

I want to estimate the weekly standard deviation of a lognormal process in a usual setup. $$ \frac{dS}{S} = (\dots) dt + \sigma dW $$ where $\sigma$ is a constant and $W$ a brownian motion. The ...
0
votes
1answer
172 views

beginner portfolio statistics - annualized volatility of multi-asset portfolio

Sorry for the dumb question, but I wanted to make sure my understanding of what I read and compiled was correct! I am trying to calculate the variance-covariance matrix, and annualized volatility of a ...
1
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0answers
26 views

Identifying primary share class of U.S. firms and deleting excess observations

I have a fairly large dataset of CRSP firms with their daily closing prices from 2006 till 2017. I need to filter the data so that I have one daily observation per unique firm. I've identified the ...
1
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0answers
60 views

Statistical methods to compare two financial series data

I have two financial series data, x and x', where x' was formed form ...
0
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0answers
36 views

Joint hypothesis tests

When running regressions, $$Y_t=\alpha+\beta_{9}x_{9,t-1}+\beta_2x_{2,t-1}+\beta_3x_{3,t-1}+\beta_4x_{4,t-1}+\varepsilon_t (1)$$ $$Y_t=\alpha+\beta_1x_{1,t-1}+\beta_2x_{2,t-1}+\beta_3x_{3,t-1}+\...
2
votes
1answer
33 views

Deriving the long-horizon predictive regression and hypothesis testing

I am working on the long-horizon regression, $$y_{t,K}=\mu+\beta_1x_{1,t-1}+...+\beta_nx_{n,t-1}+e_{t} $$, where $$y_{t,K}=y_{t}+y_{t+1}+...+y_{t+K-1}$$ and there can be multiple x's. So I am ...
4
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0answers
140 views

Implementing Hanson`s LMSR with Limit Orderbooks

I am trying to integrate Hanson's LMSR (see (see logarithmic market scoring rule)into an order-book with traditional bid/ask-limit orders (in KDB+/Q). The following functions define the basic LMSR ...
1
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0answers
47 views

Correlation between a sector and MSCI ACWI returns

I have daily return data of 11 sectors of MSCI World Index and the MSCI ACWI index. I want to know the stationarity of correlations between the sectors and MSCI ACWI index. This is what I have done: ...
0
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0answers
24 views

Informal definition of the almost complete convergence

I'm searching for the informal definition of the almost complete convergence (P. L. Hsu and H. Robbins (1947), Dugué (1955)), which means a definition without any mathematics formula. Thank you for ...
3
votes
2answers
262 views

Filtering smallest eigenvalues

In Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors [1], which introduces minimum torsion bets, Meucci gives an example involving the computation of covariance matrices on ...
-4
votes
1answer
114 views

For a trading strategy how many trades have to occur for statistical significance [closed]

I created a strategy using a regression on a price series. I tested it with many walk-forward analyses and it has passed. I am currently live trading it with real capital (the ultimate test). My ...
1
vote
0answers
33 views

Negative abnormal stock return and permanent impact

Assume we have a day where stock price falls many standard deviations of the mean (e.g >3) . How could we test, in terms of time-series, if this negative shock is permanent or deminishes in the long ...
1
vote
2answers
91 views

Calculating implied volatility from moneyness/volatility values for date

For an option expiring at a particular date I have Moneyness 0.4,0.7,0.85,0.95,1,1.05,1.15,1.3,2.5 Vol 0.105,0.075,0.045,0.045,0.202,0.045,0.045,0.075,0.085 ...
1
vote
0answers
37 views

Trading rules: Controlling the portfolio FDR+ level

I'm trying to apply the FDR+ (False Discovery Rate +) methodology from Bajgrowicz (2011) link another_link. I have computed the p-values with the stationary bootstrap as they did, however I am not ...
1
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0answers
35 views

Bootstrapping to Judge the Fit of a Sampled Return Distribution

Consider the following: I have sampled yearly stock returns from a specified distribution. What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly ...