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.

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2
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2answers
136 views

What are the proper metrics to look at for checking discrepancies in these two time series

I am obtaining bid/ask price and volume market data from two different sources for the same ticker and for the same day and checking to see that at time intervals X they are "roughly the same". The ...
0
votes
2answers
136 views

Use of geometric mean for average return of several indices

Can anyone give any reference for using the geometric mean to average the returns from several indices? Note, this question is not about the usual use of geometric mean to obtain the average return ...
6
votes
2answers
392 views

Efficiency vs. Robustness - To use a constant or not in single factor time-series regression?

Arbitrage pricing theory states that expected returns for a security are linear combination of exposures to risk factors and the returns on these risk factors. Betas, or the exposures of the security ...
2
votes
2answers
231 views

Measuring historical earnings surprises, their frequency and severity

This is my first post to Quantitative Finance, so I hope my question is formatted the right way. I am starting to research the effects of earnings surprises on certain equity indices. Is there a ...
-1
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0answers
16 views

How to estimate a value for 2 categories with 2 different weights

So I have multiple categories with lets say an X and Y, Revenue and Trade Spend. 1: x=2,000,000 y=400,000 2: x=50,000,000 y=10,000,000 3: x=100,000,000 y=20,000,000 so on... so N: x=5y; y Let's say ...
4
votes
3answers
6k views

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 ...
7
votes
4answers
435 views

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 ...
14
votes
5answers
5k views

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 ...
1
vote
0answers
37 views

Properties of a Symmetric Copula

I am working with the following copula, and have a few questions about it: $C(x,y) = xy + \theta (1-x)(1-y)xy$ Here $\theta \in [-1,1]$ and $x,y \in [0,1]$ First, I am trying to show this copula is ...
1
vote
3answers
157 views

Calculate correlation between two sub portfolios and the combined portfolio

I have two sub portfolios (lets call them portfolio a & portfolio b - a portfolio is just a vector of weights that sum to 1) that combine to create a total portfolio. I also have a 2 x 2 ...
6
votes
2answers
228 views

Why do I have a statistically significant slope regressing R(t) on R(t-1)

I am reading Cochrane's lecture note here He mentioned that when you regress annual return on time t on that of time t-1, you will have neither statistically significant nor economically significant ...
3
votes
1answer
156 views

a good book on option pricing from theoretical and practical aspect

This is the situation someone I know is in: She has good understandings of stochastic calculus and the very basics about black-scholes and binomial model, but nothing more. Her background is in ...
9
votes
5answers
5k views

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?
2
votes
1answer
139 views

How to compare different volatility measures?

I read the Euan Sinclair's book (Volatility trading) in which he suggests different volatility estimators (Close-to-close, Parkinson, Garman-Klass, ...). I am inquiring about what is the best stock ...
19
votes
4answers
5k views

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 ...
9
votes
3answers
2k views

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 ...
0
votes
0answers
58 views

Sampling and/or asymptotic distribution of a function

Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
2
votes
1answer
87 views

Summary statistic for the average probability of default?

I have the following scenario: Let $X_i$ denote the event where some institution $i$ 'defaults' (don't worry about the exact definition of a default here, it is not relevant to the question at hand). ...
0
votes
2answers
156 views

Estimate weekly, yearly quantities from finite samples

I'd like to estimate from a daily prices serie $P_t$ with $N$ observations a quantity such as the variance of the weekly returns. I will use $\ln\left(\frac{P_{T+5}}{P_T}\right)$ assuming 5 days in a ...
5
votes
2answers
475 views

What are the econometric assumptions in the Fama-Macbeth procedure (1973)?

Fama-Macbeth (1973) introduce a two stage cross-sectional regression method (http://en.wikipedia.org/wiki/Fama%E2%80%93MacBeth_regression). 1) If I was to regress stock prices (or returns) on a ...
0
votes
1answer
106 views

Calculating the Sum of Squared Deviations between two Normalized Price Series

How can I calculate the sum of square deviations between two normalized price series according to (Gatev et. co 2006)? My normalized price series of stocks $X$ and $Y$ consist of the cumulative total ...
6
votes
2answers
212 views

Co-integration constraints of coint(X,Z) given coint(X,Y) and coint(Y,Z)?

The Augmented Dickey-Fuller Test can be used to measure how well ranked certain pairs are against others for co-integration. So then say we have a known co-integration between ...
3
votes
1answer
248 views

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?
2
votes
0answers
104 views

Correlation between idiosyncratic residuals and forward returns

The classic mean-reversion strategy is to calculate an "expected return" (alpha) by computing the raw return for each security and then remove the part which you think is market driven. Statistically ...
-1
votes
1answer
116 views

Calculate the total returns from the total return index [closed]

I have the Total Return Index(RI) for several companies. I know that I can calculate the log retunrs with $ln(RI_t/RI_{t-1})$. Therefore my first guess would be to ...
2
votes
1answer
121 views

Are my estimates of parameters of geometric brownian motion correct?

I wrote a simulation of a geometric Brownian motion which works like this: ${ t }_{ i }-{ t }_{ i-1 } \sim Exp(\lambda )$ ${ Z }_{ i }\sim N(0,1)$ ${ Y }_{ i }\sim { e }^{ \sigma \sqrt { { t }_{ i ...
10
votes
3answers
406 views

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 ...
1
vote
1answer
237 views

Probability of a return from historical average and standard deviation

I have a question from a sample exam paper that I'm having some trouble figuring out. The question is: Bavarian Sausage stock has an average historical return of 16.3% and a standard deviation of ...
5
votes
0answers
116 views

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 ...
11
votes
5answers
3k views

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 ...
7
votes
1answer
456 views

How to model time series of illiquid stocks - 400 observations (transactions) per 8 hours?

How to model time series which are illiquid - 400 observations (transactions) per 8 hours ? Are there models suitable for this situation which incorporate not only size of the transactions but also ...
4
votes
2answers
355 views

Differential equation for log-returns

I have a question that might be trivial to most of you, but somehow I'm not able to solve it by myself. I have a disagreement with my colleague on the distributional properties of a Geometric Brownian ...
0
votes
0answers
22 views

definition of high frequency data [duplicate]

i would like to know what does mean high frequency data and low frequency data?there i could not find any basic definition of these two term,also it is very important to know what is meant by mean ...
2
votes
1answer
398 views

Monte Carlo Options Probability Calculation

I have a fairly simple problem for an application I am writing currently. How do you calculate the options probability of being in the money or touching a certain strike price. I know there are at ...
2
votes
0answers
254 views

Is this methodology to calculate Alpha using multi-factor regression model correct?

I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. ...
3
votes
0answers
147 views

Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?

I have several assets, each with different return histories. Some of the assets have 75 days of return history, others have 40 or so days. In calculating a robust covariance matrix, should I be using ...
0
votes
0answers
80 views

Penalize outlier values in time-series (Squaring, CoV)

I have set of log-return values. For this set need to calculate Coefficient of Variation with outlier values penalization. I'm just squaring all values to penalize outliers and there are different ...
1
vote
2answers
490 views

Partial Least Squares Discriminant Analysis

Could anyone point me to detailed literature about "Partial Least Squares Discriminant Analysis"? Intuition, methodology and examples.. Thanks,
10
votes
1answer
307 views

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 ...
10
votes
5answers
1k views

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 ...
4
votes
1answer
161 views

Statistical Power and Active Management

I was reading an article recently that pointed out the dangers of using statistical inference in evaluating active managers as the power of statistical tests diminishes with the variance of the ...
0
votes
1answer
102 views

Calculating company-level market capitalisations from share quantities and values

I want to calculate company-level market cap values for stock exchanges listed by Bloomberg. I gather this can be calculated as the product of share price and the total of shares in circulation. But ...
0
votes
1answer
99 views

Analyst Forecasts for monthly unemployment rate

Are there any resources that tabulate past analyst forecasts for the monthly unemployment rate along with the dispersion of the forecasts
2
votes
0answers
223 views

Market risk stress testing?

I am doing a research for a paper for market risk stress testing. In fact I found some information on the web about this important topic such as: Stress Testing from Art to Science Stress Testing ...
0
votes
0answers
231 views

Simple EOD computations for tick data

As part of End-Of-Day calculations once a particular market/exchange has closed for all the tickers traded on that market one may typically compute the following properties: OHLC Bid/Ask Price ...
3
votes
0answers
401 views

How to determine ratios for mean-reverting basket

Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model: ...
2
votes
1answer
573 views

Predict Quadratic Trend in Time Series

Can anyone kindly point out if I made any mistakes in making predictions using quadratic regression model in time series? I called the predict() function with the appropriate data vector and model, ...
1
vote
1answer
151 views

help me compare methods to compute one instrument price from another instrument price

Assume we have two instruments A and B. Also time is increasing from 1 to n. Let's say that ...
1
vote
2answers
144 views

Statistics of difference between two GBMs

if I have two asset prices modeled separately as geometric brownian motions. How do i go about calculating the expected statistics of their difference? Like given the sigmas and mus of both processes, ...
1
vote
1answer
367 views

Testing Significance of Correlation

Lets say I have the returns of two stocks(stock1 and stock2). Now without running a regression, I lag one of the variables, calculate the correlation between the two stocks and repeat this process as ...