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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4 views

How to calculate the standard deviation of a 'deviation from a moving average'?

Say I have a vector of daily price changes for an asset and calculate the standard deviation of returns in the usual way. Let's call this result A. Now assume that for the same asset I also have a ...
5
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4answers
118 views

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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0answers
20 views

Interpretation of Cointegration results, pValues and t-Stat

This is a follow up to: Cointegration results interpretation validation? I ran another Engel Granger Test on a pair, The results I get: ...
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1answer
134 views

Stress Testing Methods

I'm working on the following task: Given quarterly data: a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages a slew of ...
15
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6answers
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 ...
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1answer
25 views

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 ...
4
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3answers
170 views

How is stock data objectively different to this random walk?

I have a random walk that is generated as so using python, numpy, and matplotlib ...
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0answers
84 views

What machine learning method is more suitable for prediction of financial time series? [closed]

I have some time series from a stock exchange market. For each of them, I want to answer the question that whether the price will grow at least p percent in the d coming days or NOT(and during these ...
5
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3answers
8k 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 ...
2
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0answers
47 views

seasonality and generalized additive model

I am reading a report which talks about seasonality. There is a chart showing the average returns for each month of the year. In the chart it appears the last 3 months of the year tend to be negative. ...
1
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1answer
83 views

detecting and measuring lead lag effect

Given two time series data. I remember there is one statistics that tells you one is the leading factor while the other is the lagging factor. However, i do not remember the exact details. correlation ...
3
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1answer
110 views

factor models and using cross section regression

I have been doing some reading on factor models. In the literature it mentions that when creating a portfolio that maximises particular attributes it may lead to unwanted bias to other factors. I ...
8
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3answers
2k views

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 ...
2
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2answers
107 views

Predict Futures Prices based on weather + agricultural data

I’m working in the area of Data Mining and have come up with the following idea for my Masters project.The text may not be the best structured but it’s a working draft to give you a quick idea. ...
2
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2answers
49 views

Is this a reasonable approach to determine the relative importance of valuation factors?

I am trying to come up with a measure of relative importance of a number of valuation factors. I am wondering whether correlation coefficients can't be used for determining this. More on the issue: ...
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2answers
57 views

How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?

in the book "Numerical Methods and Optimization in Finance" I red the following: "Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, ...
3
votes
3answers
308 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 ...
2
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0answers
82 views

State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
1
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0answers
37 views

How to value a portfolio of non-mature consumer loans?

I'm looking for the best way to value a portfolio of consumer loans that have NOT reached maturity and for which I do observe the payment/default history to date? I'm working with a large database of ...
1
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0answers
64 views

Autoregressive distributed lag models ADL(p,q) howto in preferably matlab (stata/R/python/C# etc)

Could anyone provide me the details of how to determine the lag order of the distributed lags for an ADL(p,q) model in Matlab or another statistical package (and very much preferably in combination ...
0
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1answer
126 views

Book recommendation for time series analysis

I have been trying to wrap my head around Engel-Granger test and jcitest etc. I have failed thus far. If possible can someone guide me about which books to start with and possibly reach to ...
3
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1answer
78 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 ...
6
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2answers
266 views

Why are we obsessed over normalizing financial data?

I have recently began work on some high frequency financial tick data. I have been told to 'normalize' the data as much as possible and run linear regressions through them. In fact, the data doesn't ...
2
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2answers
152 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 ...
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2answers
154 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
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2answers
412 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 ...
8
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4answers
516 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 ...
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3answers
336 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
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2answers
245 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
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1answer
248 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
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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
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1answer
168 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 ...
20
votes
4answers
6k 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
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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 ...
1
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0answers
67 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 $X_t$ ...
3
votes
1answer
94 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
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2answers
161 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
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2answers
929 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
126 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
220 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
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1answer
306 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
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0answers
114 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
156 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
164 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
419 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
319 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 ...
6
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0answers
138 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
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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
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1answer
472 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
408 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 ...