A Course on Statistics for Finance

Stanley L. Sclove

• Verlag: Chapman and Hall/CRC
• Jahr: 2018
• ISBN:
  9781315360478
• Auflage: 1
• Thema: Betriebswirtschaft
• Thema: Finanzwesen

Taking a data-driven approach, A Course on Statistics for Finance presents statistical methods for financial investment analysis. The author introduces regression analysis, time series analysis, and multivariate analysis step by step using models and methods from finance.

The book begins with a review of basic statistics, including descriptive statistics, kinds of variables, and types of data sets. It then discusses regression analysis in general terms and in terms of financial investment models, such as the capital asset pricing model and the Fama/French model. It also describes mean-variance portfolio analysis and concludes with a focus on time series analysis.

Providing the connection between elementary statistics courses and quantitative finance courses, this text helps both existing and future quants improve their data analysis skills and better understand the modeling process.

Part IV

TIME SERIES ANALYSIS

8

Introduction to Time Series Analysis

CONTENTS

8.1	Introduction
8.2	Control Charts
8.3	Moving Averages
	8.3.1	Running Median
	8.3.2	Various Moving Averages
	8.3.3	Exponentially Weighted Moving Averages
	8.3.4	Using a Moving Average for Prediction
		8.3.4.1	Smoothed Value as a Predictor of the Next Value
		8.3.4.2	A Predictor-Corrector Formula
		8.3.4.3	MACD
8.4	Need for Modeling
8.5	Trend, Seasonality, and Randomness
8.6	Models with Lagged Variables
	8.6.1	Lagged Variables
	8.6.2	Autoregressive Models
8.7	Moving-Average Models
	8.7.1	Integrated Moving-Average Model
	8.7.2	Preliminary Estimate of θ
	8.7.3	Estimate of θ
	8.7.4	Integrated Moving-Average with a Constant
8.8	Identification of ARIMA Models
	8.8.1	Pre-Processing
		8.8.1.1	Transformation
		8.8.1.2	Differencing
	8.8.2	ARIMA Parameters p, d, q
	8.8.3	Autocorrelation Function; Partial Autocorrelation Function
8.9	Seasonal Data
	8.9.1	Seasonal ARIMA Models
	8.9.2	Stable Seasonal Pattern
8.10	Dynamic Regression Models
8.11	Simultaneous Equations Models
8.12	Appendix 8A: Growth Rates and Rates of Return
	8.12.1	Compound Interest
	8.12.2	Geometric Brownian Motion
	8.12.3	Average Rates of Return
	8.12.4	Section Exercises: Exponential and Log Functions
8.13	Appendix 8B: Prediction after Data Transformation
	8.13.1	Prediction
	8.13.2	Prediction after Transformation
	8.13.3	Unbiasing
	8.13.4	Application to the Log Transform
	8.13.5	Generalized Linear Models
8.14	Appendix 8C: Representation of Time Series
	8.14.1	Operators
	8.14.2	White Noise
	8.14.3	Stationarity
	8.14.4	AR
		8.14.4.1	Variance
		8.14.4.2	Covariances and Correlations
		8.14.4.3	Higher-Order AR
	8.14.5	MA
		8....