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.
436
questions
75
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8
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Is R being replaced by Python at quant desks?
I know the title sounds a little extreme but I wonder whether R is phased out by a lot of quant desks at sell side banks as well as hedge funds in favor of Python. I get the impression that with ...
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63
votes
6
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How are correlation and cointegration related?
In what ways (and under what circumstances) are correlation and cointegration related, if at all? One difference is that one usually thinks of correlation in terms of returns and cointegration in ...
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48
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4
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What is the best way to "fix" a covariance matrix that is not positive semi-definite?
I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix).
I am ...
- 13.5k
33
votes
5
answers
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What exactly is meant by "microstructure noise"?
I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data.
It says at higher frequencies, smaller intervals, microstructure noise is very dominant.
What is ...
- 1,347
32
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6
answers
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What is the intuition behind cointegration?
What is the intuition behind cointegration? What does the Dickey-Fuller test do to test for it? Ideally, a non-technical explanation would be appreciated.
Say you need to explain it to an investor ...
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30
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11
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Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?
What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
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27
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2
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How to interpret the eigenmatrix from a Johansen cointegration test?
I ran a Johansen cointegration test on 3 instruments, A B and C.
The results that I got are:
...
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24
votes
4
answers
19k
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Why shrink the covariance matrix?
I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of ...
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23
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6
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How to fit ARMA+GARCH Model In R?
I am currently working on ARMA+GARCH model using R. I am looking out for example which explain step by step explanation for fitting this model in R. I have time series which is stationary and I am ...
- 1,397
22
votes
1
answer
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Skewness and Kurtosis under aggregation
Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness ...
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22
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5
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9k
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How do you evaluate a covariance forecast?
Suppose you have two sources of covariance forecasts on a fixed set of $n$ assets, method A and method B (you can think of them as black box forecasts, from two vendors, say), which are known to be ...
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21
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7
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How random are financial data series?
Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
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20
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2
answers
1k
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How do you correct Max Draw-Down for auto-correlation?
When returns are auto-correlated, calculating a Sharpe ratio := $\frac {mean(x)}{\sqrt{var(x)}}$, (where $x$ are the returns) is complicated, but basically solved (see, e.g. Lo (2005)). Without the ...
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19
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3
answers
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How did James Simons clinch that security prices didn't look random?
Source: D. T. Max. Jim Simons, the Numbers King. December 18 & 25, 2017 Issue
[...] In the late seventies, not long after he won the Veblen Prize, Simons founded a small investment firm in an ...
user31928
19
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2
answers
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Why is the first principal component a proxy for the market portfolio, and what other proxies exist?
Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
- 2,003
17
votes
3
answers
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Hidden Markov Model & Its Application
I have started reading about HMM it gives an intuitive idea about what HMM is all about. I am looking out for example where its applied to Equity model using R / Excel. The material which I read so ...
- 1,397
17
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4
answers
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How do I calculate the skewness of a portfolio of assets?
I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
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17
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4
answers
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How to generate synthetic FX data for backtesting?
I want to generate synthetic forex data for the purpose of backtesting my trading algorithms. I have some rough ideas in mind on how to do this:
Start with a curve representing a trend, then randomly ...
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16
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5
answers
6k
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How can I quantitatively test the validity of momentum indicators?
I am learning about quantitative finance, and I am struck by how different it is from the techniques that make it into magazines and TV, particularly technical analysis. Specifically, if they say an ...
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16
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5
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3k
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Are two identical time series cointegrated?
I did cointegration test on two identical time series, and the result shows that they are not cointegrated, but intuitively, I think they are.
Can anyone share some thoughts on this? Thanks!
user752
16
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3
answers
1k
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What are some research articles on using principle components to generate alpha?
Here's an example by Marco Avellenada from NYU titled "Statistical Arbitrage in the U.S. Equities Market". The idea of this paper involves capturing mean reversion in the residual returns of a ...
- 13.5k
16
votes
1
answer
595
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Comparing backtesting returns with real trading returns
I have 10 years of backtested simulated performance of some trading strategy (using historical prices), and N months of actual trading performance. What statistical test can I do find out if I'm on ...
- 371
16
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0
answers
399
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Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)
In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund managers....
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14
votes
2
answers
5k
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Normality assumption in Sharpe ratio
I have read that the Sharpe ratio imposes a normality assumption, but I fail to see how. Standard deviation is statistic for any type of distribution. Anyone have any ideas?
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14
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5
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6k
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How to interpolate gaps in a time series using closely related time series?
I am trying to construct a daily time series of prices and returns for some large universe of securities. However, all I have available are a monthly time series of the prices/returns (as well as ...
- 13.5k
14
votes
1
answer
3k
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How do I reproduce the cross-sectional regression in "Intraday Patterns in the Cross-section of Stock Returns"?
Recently I was trying to reproduce the results of "Intraday Patterns in the Cross-section of Stock Returns" (published in the Journal of Finance 2010). The authors used cross-sectional regression to ...
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14
votes
1
answer
818
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Has any research used Bayesian networks to estimate risk factor betas?
Is there any published research on estimating the beta of a security with respect to one or more risk factors via Bayesian networks?
I'd like to see if this is a promising angle of research.
- 13.5k
14
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1
answer
1k
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What is the Sugihara Trading System?
I recently heard the term Sugihara Trading System. I guess it might be some trading strategy or a special model to predict trends in market data, but I couldn't find out anything about it. Does anyone ...
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14
votes
1
answer
700
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How to estimate the covariance of an index with a basket of stocks?
What would be an ideal way to estimate the covariance of an index with a basket of stocks? For example, should I use one-tail ANOVA test or an individual stock & index F-test?
- 1,397
13
votes
4
answers
18k
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How to calculate the JdK RS-Ratio
Anyone have a clue how to calculate the JdK RS-Ratio?
Let's say I want to compare the Relative strength for these:
EWA iShares MSCI Australia Index Fund
EWC iShares MSCI Canada Index Fund
EWD ...
- 241
13
votes
4
answers
4k
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Bayesian or Frequentist in Finance?
I'm currently an undergrad at a Canadian university and our finance courses has been brought up through the frequentist approach (ols, hypothesis testing, sampling theory). Only recently, through ...
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12
votes
4
answers
8k
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What are the canonical books for statistics applied to finance?
I have some decent knowledge of probability, stochastic processes and option theory, however I do not have a proper background in statistics.
Now I am working quite a lot with data, and trying ...
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12
votes
3
answers
2k
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How to group timeseries showing similar curve
I am trying to classify similar looking curves of a timeseries and was wondering what is the best algorithm to research. Reading R, it looks like k-means clustering could be applied - but I don't know ...
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votes
2
answers
1k
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What is the precision of standard deviation estimates with small samples?
I was asked today to "quantify" the precision of an estimated the standard deviation from a small sample, I was not sure how to answer.
The case is quite simple, I have a sample of $n=25$ measures (...
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12
votes
3
answers
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Can the Hurst exponent be greater than one?
Can the Hurst exponent be greater than one? Does it mean that the time series follows a random walk or that it's not stationary?
- 1,397
12
votes
1
answer
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Why does the following data fail my cointegration test?
I have some closing price data for two Australian banks which track each other very closely.
http://dl.dropbox.com/u/12337149/stat/CBA.csv
http://dl.dropbox.com/u/12337149/stat/WBC.csv
Code from ...
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12
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2
answers
1k
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GARCH model, expectation of volatility?
Consider a time series $\{r_t\}$ following a standard GARCH(1,1) model, i.e.,
$$ r_t = \sigma_t \epsilon_t,$$ where $\epsilon_t \sim N(0,1)$ and are i.i.d, and
$$\sigma_t^2 = \omega + \alpha_1 r_{t-1}^...
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12
votes
1
answer
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A non parametric study of VaR with kernel density
I'm working in order to compare the calculation of the VaR between the methodology of copulas and kernel density, all this by using the software r.
The process that I follow is:
Obtain a sample (...
Michelle
11
votes
2
answers
5k
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What is the total correlation between assets in a portfolio?
Suppose I have portfolio with 10 assets, each one of them with a weight of 10% from the total portfolio (equally weighted).
It's well known how to measure from historical prices->returns a variance-...
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11
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2
answers
5k
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How can I compare distributions using only mean and standard deviation?
I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built ...
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11
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2
answers
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Annualzing the log of daily returns riddle
Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
- 13.5k
10
votes
3
answers
772
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How to test for and how to simulate price rise/fall asymmetry in the stock market
One of the stylized facts of financial time series seems to be a fundamental asymmetry between smooth upward movements over longer periods of time followed by abrupt declines over relatively shorter ...
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10
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1
answer
1k
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How are Expected Shortfall and Variance related?
I would like to know how Expected Shortfall $SF_\alpha$ and variance $\sigma^2$ are related.
If I follow what Aaron Brown answered in this post, when the underlying distribution is Normal with ...
- 11.1k
9
votes
3
answers
24k
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Kalman Filter Equity Example
I am looking out for some material where I can study about Kalman Filter applied to Equity using Excel or R?
- 1,397
9
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2
answers
1k
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What machine learning method is more suitable for prediction of financial time series?
I have time series data for various assets and which I transform to create various features. I have framed the problem as a classification task where I attempt to predict either a positive or negative ...
9
votes
3
answers
391
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How to improve the consistency of explained variance statistics in a linear equity model?
I have an intraday equity returns linear model that, overall, shows good values in terms of $R^2$, p-value and other explained variance statistics. Around 70% of the stocks show consistent R-squared (...
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9
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2
answers
1k
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Kolmogorov-Smirnov test for Generalized Pareto Distribution
I've fitted my data to a generalized pareto distribution as to model the returns in the tails more accurately. The interior is fitted with kernel distributions.
I would like to now test whether the ...
- 111
8
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2
answers
3k
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How to make the final Interpretation of PCA?
I have question regarding final loading of data back to original variables.
So for example:
I have 10 variable from a,b,c....j using returns for last 300 days i got return matrix of 300 X 10.
...
- 1,397
8
votes
3
answers
8k
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How can I estimate the degrees of freedom for a Student's T distribution?
I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I ...
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8
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2
answers
464
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How to combine various equity measures into a single measure (vector magnitude)
I have several measures:
...
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