Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
1. Time Series.
A. Time series forecasting.
B. Updating a linear forecast.
C. Kalman filter I.
D. Kalman filter II.
E. Simultaneous equations.
a. Simple linear reduction.
b. Simultaneous equations bias.
c. Two stage least squares procedure for simultaneous equations.
d. General note of applicability.
2. Classical statistics.
3. Bayesian statistics.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Simple linear reduction.

uppose the observed real valued processes of discrete time $p_{t},\,q_{t}$ are connected by the relationship MATH where the $\varepsilon_{t}$ is a Gaussian random variable with zero mean. Assume farther that we are given samples MATH and MATH . We would like to compute a maximal likelihood estimate of $\alpha$ . The log-likelihood function is proportional to the sum MATH where we use the notation MATH . Hence, the maximal likelihood estimate $\alpha^{\ast}$ has to satisfy MATH MATH Therefore, the value $\alpha^{\ast}p$ is given by the projection of $q$ on $p$ : MATH

Notation. Index. Contents.

Copyright 2007