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.
2. Classical statistics.
3. Bayesian statistics.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Updating a linear forecast.

e are interested in forecasting of quantity $y_{3}$ based on information MATH . The information comes as a flow. So, at first, we know $y_{1}$ . Based on $y_{1}$ we compute the projection MATH . Then we receive additional data $y_{2}$ and obtain MATH . Our goal here is to express MATH as a function of $y_{2}$ , MATH and MATH . Such result would provide a recursive relationship useful for general situation of long information flow MATH .

Our computation below is motivated by the fact that for $y_{1}\perp y_{2}$ we have MATH In general $y_{1}$ and $y_{2}$ are not orthogonal so we make a correction: MATH MATH MATH MATH MATH MATH

Notation. Index. Contents.

Copyright 2007