The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.

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20
votes
3answers
990 views

How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape ...
20
votes
3answers
2k views

Tools in R for estimating time-varying copulas?

Are there libraries in R for estimating time-varying joint distributions via copulas? Hedibert Lopes has an excellent paper on the topic here. I know there is an existing packaged called copula but ...
17
votes
5answers
3k views

What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?

One of the main problems when trying to apply mean-variance portfolio optimization in practice is its high input sensitivity. As can be seen in (Chopra, 1993) using historical values to estimate ...
15
votes
5answers
1k views

How to estimate the probability of drawdown / ruin?

A fairly naive approach to estimate the probability of drawdown / ruin is to calculate the probabilities of all the permutations of your sample returns, keeping track of those that hit your drawdown / ...
11
votes
3answers
1k views

How to detect regime change when estimating asset correlation from historical time series?

Suppose I have two asset time series, $X_t$ and $Y_t$, and I'm estimating their correlation from historical data. I'd like to apply some systematic criterion to estimate what time window I should use ...
11
votes
1answer
552 views

rugarch: Joint estimation leads to different results

I want to fit an ARMA-GARCH model to my data using rugarch package in R. First of all, I look at the acf and pacf: ...
10
votes
3answers
367 views

How to account for market movement when some exchanges are closed?

Daily data, such as open and close prices, is often available for much longer periods than high-frequency data. However, whenever backtesting any strategy that examines instruments traded in different ...
10
votes
2answers
444 views

How to estimate the following model?

Suppose I have the following model: $$r_t=\sigma_t * \epsilon_t$$ where $r_t$ is the return at time t, $\sigma_t$ is the volatility, the model used to model this volatility is an exponentially ...
9
votes
1answer
451 views

What good papers of short term (<30 seconds) volatility estimation [duplicate]

I am looking for good papers of short term (<30 sec) volatility estimation AND short term volatility forecasting. Do you have something in mind ?
8
votes
2answers
736 views

Fitting a generalized logistic distribution

I have a process that estimates the parameters for the following function using the NL2SOL algorithm. $C-[\alpha+\frac{\beta-\alpha}{1+e^-\theta(y_t-\delta)} \vartriangle y_t]$ The process currently ...
8
votes
1answer
812 views

Musiela parameterization

I have a question regarding the proof of the Musiela parametrization for the dynamics of the forward rate curve. If $T$ is the maturity, $\tau=T-t$ is the time to maturity, and $dF(t,T)$ defines the ...
7
votes
1answer
394 views

What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
7
votes
2answers
548 views

Estimation of Empirical Expected Shortfall of a heavy tailed distribution

Assume that you have a portfolio for which you have estimated a parametric model to the underlying instruments, but the distribution of the portfolio as a whole is too complicated to compute ...
7
votes
2answers
467 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 ...
7
votes
1answer
186 views

What tradeoff is there to using an accurate estimate with a large confidence interval?

I am working on calibrating a Heston model from simulated historical stock data. After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these ...
6
votes
2answers
211 views

What is the preferred GARCH method in practice?

My advance apologies, if this question is too naive or basic. Please be patient with my first experiences with SE; ask for clarification, if needed. I recognize there are many (often-criticized) ...
6
votes
2answers
3k views

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 ...
6
votes
0answers
140 views

Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$ dr_t = \alpha(\beta - r_t)dt + \sigma dW_t, $$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
5
votes
2answers
806 views

How to use a realized kernel?

I've read that realized kernels are the thing to use for calculating daily volatility from high-frequency data. So I've got minute data, how do I actually use such a kernel? Will it give me minute-ly ...
5
votes
2answers
121 views

Is there a relation between these two forecasting/estimation approaches?

When learning econometrics I have usually seen stuff from the following perspective: Assume $Y_t = f(X_t) + e_t$, where f is some function of $X_t$ (typically linear). For example, assume $Y_t = X_t ...
5
votes
0answers
64 views

What kind of errors arise when I fit ARMA(1,1) to data generated from ARMA(1,1)-GARCH(1,1) process?

As far as I know estimates of parameters of ARMA(1,1) are asymptotically optimal when fitted to data from ARMA(1,1)-GARCH(1,1) process, and only their variance increase, so when we assume large ...
4
votes
1answer
2k views

How do I estimate the parameters of an MA(q) process?

It is relatively easy to estimate the parameters of an autoregressive $AR(p)$ process. How do I do with a moving average $MA(q)$ process?
4
votes
2answers
89 views

Degrees of freedom in calculating significance of GARCH coefficients

I am trying to determine the significance of coefficients of a GARCH model by calculate the p-values using the following Matlab formula: pvalues = 2*(1-tcdf(abs(t),n-v)), where $t$ is the ...
4
votes
2answers
975 views

Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
4
votes
1answer
87 views

How are Quandl monthly S&P500 earnings estimates derived?

Can someone explain how the monthly earnings estimates are derived for S&P500? Quandl sources multpl.com, who state: ...
4
votes
0answers
213 views

Estimation of ranks of log-returns via copula

I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order to be ...
3
votes
2answers
231 views

What nonparametric methods exist for estimating intraday seasonalities?

What nonparametric "Model Free" methods exist to measure intraday seasonality? I would like to estimate intraday seasonality in any of The volatility The traded volume The bid ask spread or ...
3
votes
4answers
394 views

Unsmoothing of returns

The following problem arises in the context of private equity, which typically report "smoothed" returns (think of it as a moving average). As you can imagine, "smoothed" returns would have a much ...
3
votes
1answer
500 views

How to calculate tracking error given mismatches in available data

Apologies if this is an overly simple question. I have a series of stock returns, and I would like to estimate my portfolio's ex-ante tracking error versus the benchmark (S&P 500) given the ...
3
votes
1answer
96 views

Log-likelihood of skew-t distribution

I am trying to estimate GARCH models with the use of Hansen's (1994) skew-t distribution. I am using matlab's ARMAX-GARCH-K toolbox, where the log-likelihood is calculated as: ...
3
votes
1answer
300 views

Stochastic Volatility CIR estimation

Would anyone have a code (pref. Matlab or R) for any type of estimation (QML, GMM) not using option prices of a stochastic volatility model driven by a CIR process described below? \begin{equation} ...
3
votes
0answers
102 views

Derivation of variance of Zhou (1996) volatility estimator

Does anyone know how to derive the Variance of Bin Zhou's volatility estimator (Theorem 1) in 'High-Frequency Data and Volatility in Foreign-Exchange Rates' (1996) Zhou 1996 Any help would be ...
3
votes
0answers
172 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 ...
2
votes
1answer
87 views

GJR-GARCH with $\alpha = 0$ as parameter estimate

I am estimating a GJR-GARCH(1,1) model with variance targeting in R. As data I am using returns on some stock indices. While calculating the GARCH models I obtain $\alpha=0$ for some indices. From ...
2
votes
2answers
936 views

Should I use GARCH volatility or standard deviation in cross-sectional regression?

I want to do a cross-sectional study where the historical, medium-long run volatility of some return series (call it $R_t$) is included as a regressor. Which of the following two estimates of ...
2
votes
1answer
274 views

2-step estimation of DCC GARCH model in Python

Embedded in this thread are multiple questions. I'm currently im the process of implementing a DCC GARCH forecast model on quantopian (a python-powered trading platform). The two step consists of ...
2
votes
1answer
98 views

Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
2
votes
2answers
168 views

Extracting Signal from Noisy Data

Consider a scenario in which Y_t represents the % change in price and we want to use X_t to predict Y_t. We assume that X_t is information we get before Y_t is revealed. Suppose that in reality Y_t ...
2
votes
1answer
224 views

Predicting stock returns - in a panel data specification or by using portfolio formation strategies?

I'm working on an empirical analysis where I try to predict stock returns using weekly data. Ideally, I would like to use a panel data model like the following: $$ ...
2
votes
1answer
326 views

Which prices to use to compute realized volatility?

For computation of realized volatility, especially range based volatility, deal prices are commonly used. If Level I data available should the deals data still be used or another measures of spot ...
2
votes
1answer
664 views

How does the CME set margin requirements on commodity Futures

I am trying to model margin requirements on various commodity futures, however it doesn't seem that the CME has released the formula they use to set these performance bonds. I am sure that they use ...
2
votes
1answer
137 views

How to reconstruct a discontinued economic time series such as the Fed's CP rate?

The old 3-Month Commercial Paper Rate (CP3M) on FRED was discontinued in 1997. I would like to reconstruct this series in a reasonable fashion, so I can use it to analyze more recent events. I was ...
2
votes
0answers
38 views

How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
1
vote
1answer
193 views

Basics about the scaling property of volatility

It is a usual practice to calculate realized volatility $\sigma$ using the square root of the usual variance estimator $\hat{{\sigma}²}$. This is done using the stock log returns (practitioners ...
1
vote
1answer
15 views

Measure difference between estimations and historic returns

For every day in a year, I have the return on an asset and the CAPM estimation for the return. I want to measure the average difference between the set of returns and set of estimations. So far, I ...
1
vote
0answers
53 views

How to fit exogenous + GARCH Model In Python?

I am studying a textbook of statistics / econometrics, using Python for my computational needs. I have encountered GARCH models and my understanding is that this is a commonly used model. In an ...
1
vote
0answers
101 views

Skewed Generalized Error Distribution's (SGED) pdf

I want to use the SGED distribution of Theodossiou for GARCH estimation, however, I am struggling to understand which is the correct pdf function of the distribution. Let me just say that the ...
1
vote
2answers
148 views

How to estimate probable seeling pricegiven OHLC data for backtesting?

I'm relative new to this, so I might be asking something that doesn't make sense. Here is my scenario: I have intraday day at 1 minute intervals. This data has ohlc data and I want to compute for any ...
1
vote
0answers
54 views

What are the estimation methods for SV models?

I want to know about some methods like Methods-of-Moments, Quasi-Maximum Likelihood method, Baysian methods using Markov Chain Monte Carlo methods. Is there any reference to have an idea of these ...
1
vote
0answers
99 views

Derivation of a ML estimator

I have the following likelihood function: I'm given this information about the $\Omega$ matrix ($\boldsymbol{1}$ is a $T \times 1$ vector of ones): I would like to be able to show that the ...