Questions tagged [estimation]
The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.
0
votes
0answers
25 views
How to fit and test VaR in R
I have estimated the below model with gjr-garch11
gjrgarch11n.spec = ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder=c(1,1)), mean.model = list(armaOrder=c(1,0), include.mean = TRUE),
...
3
votes
1answer
88 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
77 views
How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?
Introduction
My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
0
votes
0answers
19 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 ...
0
votes
1answer
115 views
Which program for a DCC-MIDAS model?
for a thesis research, I plan to use a DCC-MIDAS model. The program I was working with (STATA) is not able to run this.
Do you have any suggestions as to which program is best for this analysis?
...
1
vote
1answer
146 views
How to estimate lambda for Jump-Diffusion Process from Empirical data?
So, I have really no idea how to go about this, but how would I go about choosing sensible parameter values for a basic jump-diffusion simulation, namely $\lambda$ ?
For example, getting the average ...
1
vote
0answers
161 views
Fama French- typical time lag
I have daily prices of 400 stocks for the last 10 years. I have to create each month a portfolio of 20 stocks that minimizes variance with 2 approaches:
1) Estimate volatility with a GARCH(1,1) model ...
3
votes
2answers
194 views
Estimation Risk-Neutral Variance of Returns
I am trying to find a method which allows me to estimate $Var_{\mathbb{Q}}\left(\frac{S_{t_{i+1}}}{S_{t_i}}\right)$ where $S$ denotes the price process of an underlying stock (which has to be assumed ...
6
votes
0answers
75 views
Estimation of right truncated poisson process
I have following problem:
Imagine I generate large number of homogenous poisson process sample paths (by sample path I mean a sequence of arrival times $\tau_i$ all with the same intensity. However ...
1
vote
1answer
142 views
Electric power price parameter estimation
currently I am working through the paper of Tino Kluge "Pricing Swing Options and other Electricity Derivatives" to get a better understanding about the power markets.
The author establishes methods ...
1
vote
0answers
209 views
Estimating parameters of the Cox-Ingersoll-Ross model using CLS in R
I'm working on a project where I need to estimate the parameters of the CIR model. In the particular case, the CIR model is used to model cumulated capital calls for a private equity fund.
The data ...
2
votes
0answers
26 views
Understanding pooled VAR model
I encountered a paper by Vuolteenaho (2002) in which he uses pooled VAR model. I have some troubles understanding the idea. He uses firm level variables (log returns, ROE, etc.) and ultimately he ...
3
votes
1answer
76 views
Bond yield to maturity vs current interest yield
How close is yield to maturity usually to current interest yield? Can I use yield to maturity to approximate current interest yield of a bond index?
I am trying to calculate bond index price returns ...
1
vote
0answers
37 views
How to estimate bond price returns via an index?
Let's say I have a corporate bond, for which I know current yield, modified duration, coupon and maturity. I want to estimate how it would have performed under certain market conditions by looking at ...
1
vote
2answers
135 views
How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc
I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy.
Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do ...
0
votes
0answers
70 views
Monte Carlo volatily
I was wondering if we could do a forecast on volatility using monte carlo on an underlying asset. For example EUR/USD :
Simulating a lot of possible paths on 1 year
then calculate the volatilty for ...
1
vote
1answer
72 views
Estimate American-style option delta from similar options
I have a data set which looks something like this, referring to American-style put and call options:
...
1
vote
1answer
200 views
Joint estimation of GARCH models with ARMA terms in the conditional mean: a necessity?
Supposing I am using the following models to forecast conditional volatility of index returns, whereby In-sample data is 1996-2007 and out of sample data is 2007-2012, using GARCH type models.
I have ...
3
votes
1answer
166 views
Estimating implied volatility of an index component with no vanilla options market
There are liquid vanilla options trading on an index of 20 equity components.
The question is how to price an option on one of the index components, knowing that there are no options trading on that ...
0
votes
0answers
67 views
Approximating an SDE for Volatility Estimation
Consider the SDE
$$
dT(t) = ds(t) + a(s(t) - T(t))dt + \sigma dW(t)
$$
where $s(t)$ is a deterministic function that turns out to be the long-term mean (this SDE is used to model daily temperature, so ...
3
votes
1answer
384 views
How to approximate the Carr-Madan decomposition formula?
I have came across the excellent answer.
I'm looking for a dicrete approximation of the Carr-Madan decomposition formula of the function $f(F_T)$ of the terminal futures price by taking a static ...
1
vote
1answer
98 views
Combine EWMA or ARCH model with estimator other than squared returns
Currently I use the EWMA model with the squared logarithmic returns as proxy estimator for the volatility, in order to forecast the volatility one step ahead in an intraday scenario (time frame is a ...
1
vote
1answer
104 views
What volatility estimator for continuous data and small time window?
I want to know which volatility estimator should I use for the following scenario:
I am implementing a market making bot and therefore I need to make estimations of the volatility of the price in ...
3
votes
2answers
277 views
How to estimate the variance of this stochastic process?
I have an unobservable stochastic quantity $\lambda(t)$, which I analytically know the variance of, that is
$$\text{Var}(\lambda(t))= \frac{\theta \sigma^2}{2\kappa}$$
My goal is to get an estimate ...
3
votes
1answer
103 views
Streaming update of the GARCH(1,1) model
Given the estimate of GARCH(1, 1) model parameters I observe the new price. How to update the estimate with this new information.
Let's assume I know the coefficients that maximize the likelihood ...
4
votes
4answers
253 views
Compare two time series with different frequencies
Lets say I have two time series $X_t$ and $Y_{t,q}$. As an examples, lets say $X_t$ is a series that measures year over year changes in the level of output of a good (say number of widgets). So $X_t = ...
1
vote
0answers
193 views
Relationship between in-sample and out-sample periods length
I have two general questions regarding "in-sample fitting vs. out-of-sample backtesting" kind of analyses. Is there any relationship between the length of the data collected for in-sample fitting ($a$)...
1
vote
1answer
374 views
What is Estimation Risk - VAR Backtest
Simple Question. Can someone explain please: What is Estimation Risk in Value at Risk Backtesting
0
votes
0answers
38 views
is mean and variance sufficient to determine the following question?
consider this question: I want to buy AAPL, and I could buy it from 3 brokers. I have their historical quote. Is there any statistic other than mean and variance I could use to determine if one broker ...
1
vote
1answer
1k views
Package for multivariate Garch Vech model for R?
I`m new to programming and searching a package for R which inherents the estimation for a Vech Garch(1,1). This is a multivariate Garch model which forms the residuals and the covariance matrix from a ...
4
votes
2answers
783 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 t-stat, $...
1
vote
0answers
451 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 ...
2
votes
1answer
306 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 ...
1
vote
0answers
843 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 ...
0
votes
1answer
125 views
How to estimate today's closing price?
I'm working on interday trading algorithm and I have a basic question:
How can I estimate today's closing price? I need it to predict tomorrow closing price. Should I use the price few moments before ...
0
votes
0answers
405 views
Skewed Generalized Error Distribution in GARCH modelling
I am trying to estimate GARCH models with the use of Theodossiou's (2000) Skewed Generalized Error Distribution. I am modifying matlab's ARMAX-GARCH-K toolbox to calculate this model. I am calculating ...
3
votes
1answer
626 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:
...
0
votes
1answer
53 views
Imposing MLE restrictions by logistic mapping
I am doing some Maximum Likelihood Estimation with a density that has time-varying parameters. I am using the fmincon function in Matlab, but I do not know how to ...
10
votes
0answers
1k 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 ...
6
votes
2answers
387 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) ...
1
vote
2answers
191 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 ...
2
votes
0answers
46 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 ...
4
votes
2answers
341 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:
...
2
votes
1answer
2k 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
1k 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
519 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 =...
5
votes
2answers
124 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 *...
1
vote
1answer
22 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 ...
4
votes
4answers
2k 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 ...
6
votes
0answers
113 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 ...
