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14
votes
2answers
1k views

Parameter estimation of Ornstein–Uhlenbeck and CIR processes

I would like to estimate Ornstein–Uhlenbeck process' parameters via Kalman filter. My process is the following one: $\text{d}x_{t}=\alpha(\theta-x_{t})\text{d}t+\sigma\text{d}W_{t}$ I'm interested ...
9
votes
0answers
217 views

Covariance estimation: shrinkage, random matrix theory, what else?

Shrinkage was much en-vogue before random matrix theory (RMT) took everybody's attention in covariance matrix estimation, however the latter also showed its limits. A plethora of other estimators has ...
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
2answers
92 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
1answer
379 views

Ornstein versus AR(1) for modeling stationary data

I've come across several posts regarding parameter estimation for O-U models given some stationary data (say, some sort of mean reverting spread), but I can't seem to find an answer as to why modeling ...
3
votes
2answers
180 views

How to get around flat likelihood function when calibrating GBM parameters?

I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion, $$\log(S_t) = \log(S_{t-1}) + (\mu - 0.5*\sigma^2) \Delta t + \sigma*\sqrt{\Delta t}*Z_t$$ where $Z_t$ ...
3
votes
0answers
192 views

Time series (stochastic process) estimating parameters using characteristic function

I have a time series of assets ${A_1, A_2, ..., A_n}$, which is described by a sophisticated distribution having the following characteristic function: $\phi(u; t;\theta)$, where $\theta$ is a vector ...
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 ...
1
vote
1answer
113 views

Calibration of non-mean-reverting OU process

I'm looking for some reference on how to calibrate a non-mean-reverting Ornstein-Uhlenbeck process to historical data using MLE or OLS. The model has the following SDE: ...
1
vote
0answers
37 views

Texts on the Generalized Method of Moments

I was looking for a book that could explain me well the Generalized Method of Moments, its mathematical nuances, and even have a look to the empirical side, maybe with some guided exercises with Stata ...
0
votes
1answer
83 views

Local volatility parametrization using the spot

Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ? Any help would be appreciated.
0
votes
1answer
58 views

Kalman Filter in Interest Rate Models

A couple questions regarding the use of Kalman filtering in estimating parameters of short rate models: 1) In Duan & Simonato (1995), which seems to be one of the earliest applications of the ...
0
votes
1answer
37 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 ...
0
votes
0answers
7 views

How to reduce variance of mean reversion estimator with maximum likelihood?

I estimate the parameters of an Ornstein-Uhlenbeck process with Maximum Likelihood. The mean reversion speed estimator is well known to be biased. There are methods to reduce the value of the expected ...
0
votes
1answer
36 views

How to estimate parameters for 2 correlated Ornstein-Uhlenbeck processes with maximum likelihood?

I would like to use maximum likelihood to estimate the parameters of two correlated Ornstein-Uhlenbeck processes from empirical data. Do you have any good references for this? If you have any hints as ...