Questions tagged [estimation]
The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.
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Fitting a multidimensional Ornstein-Uhlenbeck pProcess
If I have a dataset X, where each row is a time point and we have several variables, say 100, (so this is a multivariate time series), what is the best way to fit a multidimensional Ornstein-Uhlenbeck ...
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Residual Function
In a time series with OLS regression curve Y-hat (rolling linear regression), and with n=20, what can I say about this transformation? This formula is similar to a differential dY/dt minus an integral ...
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FX portfolio MV estimation for undelying Spot move
In the context of a project involving FX derivatives, I am faced with the challenge of estimating the change in the market value of my portfolio in response to a change in the underlying spot.
The ...
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To estimate the parameters when only the characteristic function is known to us
Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data.
To obtain VGSA, as explained in Carr et al. [2001], we take ...
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In which context do hedge funds use the Gauss Markov Theorem?
Hedge Funds really like asking questions about linear regression during interviews. Especially about the properties of the OLS. But I don't understand in which context this is used. For example the ...
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What quantities (means, betas) must be constant over time for the GRS test to be valid?
I am interested in testing the CAPM using the GRS test. Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test amounts to ...
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Resource recommendations: Levy process estimation using programming languages
Perhaps this type of question is not very suitable for this forum, but I'll try to make my question a little useful.
I'm studying stochastic processes, more precisely, Levy processes. A Levy process $...
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Stochastic volatility estimation in R
Can anyone help me with the stochvol package in R? I estimated the volatilities using this package but I am not being able to understand how to download the ...
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R resources for GMM estimation and testing of multifactor asset pricing models
Has anyone seen R script for GMM estimation and testing of asset pricing models such as Fama-French 3-factor or similar? Ideally, I would like to have R scripts corresponding to Cochrane "Asset ...
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Estimate Open, High and Low prices from bid, ask and close prices
I know it's possible to efficiently estimate bid/ask spreads from OHLC prices and there are several methods to do so. However I have a data source that contains only bids, asks and close prices, no ...
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Estimation of the Vech HAR model (Multivariate HAR)
I am trying to use the Vech-HAR (the mulitvariate HAR) model in order to forecast some covariances.
I have been looking into the model proposed by Chiriac Modelling and forecasting multivariate ...
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Incorporating idiosyncratic risk as a pricing factor with GMM
Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing an augmented CAPM or a multifactor model with an additional factor: the ...
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Definition and estimation of $\beta$: raw or excess returns?
The CAPM is a single-period model that says
$$
\mathbb{E}(R^*_i)=\beta\mathbb{E}(R^*_m)
$$
where $R^*_i:=R_i-r_f$ is an asset's excess return, $R^*_i:=R_m-r_f$ is the market's excess return and $\beta:...
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Testing the CAPM: does GRS account for errors in variables (measurement error)?
Suppose we are interested in testing the CAPM using the GRS test. Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test ...
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GMM estimation of the CAPM: why not include sample mean of the market excess return as a moment?
I am trying to wrap my head around GMM estimation of a single factor model such as the CAPM. I started by asking How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)? ...
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How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)?
Reading Cochrane "Asset Pricing" (2005) section 12.2 (p. 241), I got lost in the derivation of the GMM estimator for the single-factor model. Equation $(12.23)$ says the moments are
$$
g_T(b)...
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Clustered vs. GMM-based standard errors: which ones to use in asset pricing?
Consider estimating an asset pricing model such as the CAPM or a multifactor model using monthly data. Petersen (2009) section "Asset pricing application" suggests use of standard errors ...
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Imposing diagonality of error covariance matrix when the CAPM holds
Assuming that the CAPM holds, the total risk of an asset can be partitioned into systematic risk (associated with the market factor) and idiosyncratic risk. Idiosyncratic risk is asset specific. Does ...
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Why estimate the (known) market return in the cross-sectional regression of Fama-MacBeth?
Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing the CAPM. Using Fama-MacBeth style analysis, we first estimate $N$ time ...
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Incorporating idiosyncratic risk as a pricing factor Fama-MacBeth style
Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing the CAPM or a multifactor model. Take the CAPM:
$$
r^*_{i,t}=\alpha_i+\...
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1
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Filtering SDE for Heston Volatility
Consider a GBM model with Heston volatility:
$$dS_t = \mu S_t dt + \sqrt{V_t} S_t dB_t^1$$
$$dV_t = \kappa(\theta-V_t)dt+\xi \sqrt{V_t}dB_t^2,$$
where $(B_t^1, B_t^2)$ is a correlated BM. Let
$$\...
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Estimating Zero Coupon Curve using only Fixed-Coupon bonds available
Today I have been struggling with something that someone here for sure has already encountered. I have a corporate issuer with a set of fixed coupon bonds (maturities between 1.5 to 20+ Years, luckily ...
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Estimating the relationship between short-term intretes rates and 10Y bond yields
On the 16th of March 2020, the Polish Central Bank announced its first-ever round of Quantitative Easing. I am conducting an event study on how this announcement impacted the term structure.
The main ...
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2
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Estimating historical volatility from inconsistent time intervals
Given historical asset prices at consistent time intervals, one can estimate annual volatility as:
SampleStDev(log(Si/Si-1)) / sqrt(interval)
What's the correct way to do this when the time intervals ...
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Estimate market positioning from flow data
I have a set of time series data from a bank that is transaction data from all its clients on a particular currency.
From that data, I attempt to estimate the current "position" of all ...
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2-step system-GMM for static panel models?
Could we use the 2-step system generalized method of moment (GMM) for static regression models? As I know, 2-step system GMM is designed for dynamic panel data models but I see many papers use it for ...
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How to annualize kurtosis of returns (in simple terms)?
I'm confused by this post on how to annualize kurtosis. I don't understand how to apply it to annualize the kurtosis for my data. In other words, if I evaluated the kurtosis of, say, monthly returns (...
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A Bayesian-Stein based expected return estimator by J.P. Morgan
Please consider the following estimator for the expected returns specified in the paper "Improving on risk parity: Hedging forecast uncertainty" by Peter Rappoport, J.P. Morgan, October 2012....
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Correct terminology - estimate or model?
I am doing some academic work and I'd like to summarise the picture around volatility models. As such, I'd like to refer to several ways of estimating volatility and I'd like to use proper terminology....
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Calibrating OU parameters using AR(1)
I have a mean reverting time series and want to find the Ornstein-Uhlenbeck (OU) parameters of it. I researched the internet and found that we can calibrate the model as a simple AR(1) process,
$$\...
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Estimating the variance of returns with aggregated data
Say I have an asset return time series:
Jan2020: -5%
Feb2020: +5%
Mar2020: -5%
Apr2020: +5%
May2020: -5%
Jun2020: +5%
Q3 2020: +20%
Oct2020: +5
Nov2020: -5
Dec2020: +5
Note that 3 months of data is an ...
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How does yahoo calculate Growth Estimates
Does anyone know how yahoo calculates Growth Estimates for the Next 5 Years (per annum)? For example, I can see 12.64% for AAPL as reporetd in Yahoo finance in https://finance.yahoo.com/quote/AAPL/...
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Mean estimate in portfolio optimization (Markowitz) [duplicate]
The Markowitz mean-variance portfolio optimization problem is to find the optimal allocation, $w_{optimal}$ by solving:
\begin{equation}
w = \mathrm{argmax} \ \mu_{t}^Tw - \frac{\gamma}{2}w^{T}\...
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Entropy-implied volatility requires itself to be calculated?
\begin{align}
H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\
&= \frac{1}{2} \ln (2\pi e \sigma^2)
\end{align}
is the analytical solution for the entropy of a Gaussian random variable, ...
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Estimating constant and local volatility based on passage times
Consider a Brownian motion B_t with constant instantaneous volatility σ and zero drift
where ...
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Do portfolio mean and portfolio variance have probability distributions?
If $X$ is a $T\times N$ matrix of multivariate asset returns,
and $w$ is some optimal portfolio weight vector,
then the portfolio return series is $r_p = X w \in\mathbb{R}^{T}$. This return series ...
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A simple question about VaR estimation
"A 99% VaR using 1,000 (simulation) replications should be expected to have only
10 observations in the left tail, which is not a large number. The VaR estimate
is derived from the 10th and 11th ...
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Question on the use of a limit in a proof
I ran into a step in an argument that I can't quite figure out. It's basically how they use a limit that I don't seem to understand. The context is local-to-unity asymptotics in vector autoregressions,...
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Do EWMA weights remove autocorrelation in asset returns?
I know that the exponentially weighted moving average (EWMA) volatility estimator drapes a decaying weight function over historical returns in order to weight the past according to the decay of their ...
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Why is asset volatility easier to estimate than the asset mean if it contains the mean?
It is well known that the variance of asset returns, $\sigma^2$ (whose square root is volatility), is easier to estimate than the asset mean $\mu$ (also known as expected return) because the mean of ...
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Do the weights of the exponentially weighted moving average (EWMA) have to sum to 1?
I am currently trying to calculate a volatility by using the EWMA model because it is said to yield better results than just using an equal weighted calculation approach. However I am a bit confused ...
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Can you approximate stochastic volatility processes using GARCH processes?
Let me specific. Suppose that you have the following process:
\begin{align}
z_t &= \sigma_t \epsilon_t \\
\sigma_t &= \sigma \exp \left( \frac{v_t}{2} \right)
\end{align}
where $v_t$...
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Correcting high AR(1) coefficients in dynamic Gordon model
I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis. However after receiving some feedback there is one last issue I want to resolve. I'm using ...
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1
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550
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Implementing Fama-MacBeth cross sectional regression
I have built a Fama and French three factors model (market excess return, small-minus-big, high-minus-low) and estimated its betas through a time series regression (code in R, but any other language ...
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Change of measure
I am looking at the derivation of the Hill estimator. It is $ \bar{F}(x) = 1 - F(x)$ the right tail of the distribution. In the derivation they use the equation
$$ \frac{1}{\bar{F}(u)}\int\limits_u^\...
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Are asset return means difficult to predict because they have no lower bound?
In finance, it is widely known that the volatility of asset returns ($\sigma$) are easier to predict than the expected value of asset returns ($\mu$) , otherwise known as the average return or mean.
...
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Are intraday volatility estimators useful for close-to-close predictions
I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
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How to predict realised variance?
I am trying to predict the realised daily close to close variance of an equity index.
I checked the literature on volatility forecasting and tried a bunch of things on a dataset for the S&P 500....
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realized correlation estimation
I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: On covariance estimation of non-synchronously observed diffusion processes, 2005) and there's something ...
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Beta estimates of Regressions on AR(1) Process
I am currently working through the paper The Myth of Long-Horizon Predictability [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of ...
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