1.        Construction of empirical models

1.1    Review of Basic statistical concepts

1.1.1           Introduction

1.1.2           Point estimation with emphasis on measures of quality

1.1.3           Interval estimation

1.1.4           Tests of hypothesis

1.2    Estimation for complete data

1.2.1           The empirical distribution for complete individual data

1.2.2           The empirical distribution for grouped data

1.3    Estimation for modified data

1.3.1           Means, variance and interval estimation

1.3.2           Kernel density models

1.3.3           Approximations for large data sets

2          Parametric statistical methods

2.1    Parameter estimation

2.1.1           Methods of moments and percentile matching

2.1.2           Maximum likelihood estimation (individual, grouped, censored and truncated data)

2.1.3           Variance and interval estimation

2.1.4           Non-normal confidence intervals

2.2    Model selection

2.2.1           Introduction

2.2.2           Representation of the data and model

2.2.3           Graphical comparison of the density and distribution functions

2.2.4           Hypothesis testing

2.2.5           Selecting a model

3          Simulation and Bootstrap

3.1    Simulation

3.1.1           Basics of simulation

3.1.2           Examples of simulation in actuarial modeling and finance

3.2    Bootstrap

3.2.1           Introduction to bootstrapping

3.2.2           Bootstrap distributions and standard errors

3.2.3           Bootstrap confidence intervals

3.2.4           Significance testing using permutation tests

4          Time series analysis

4.1    Introduction, description and classical decomposition

4.1.1           Examples of time series patterns; objectives of time series analysis

4.1.2           Component models: additive and multiplicative

4.1.3           Moving averages filtering: estimating trends and seasonality

4.1.4           Sample autocorrelation function and serial dependence

4.2    Stationary and integrated processes

4.2.1           Definition of second-order stationarity: autocovariance and autocorrelation functions

4.2.2           White noise process and the general linear process

4.2.3           Integrated processes: the random walk

4.2.4           A note on spurious time series regression and cointegration

4.3    Stationary models: autoregressive (AR) , moving average (MA) and mixed (ARMA)

4.3.1           Autoregressive models: stationarity conditions, autocorrelation functions (ACF) and partial autocorrelation functions (PACF). AR(1) and AR(2) processes

4.3.2           Moving average models: stationarity and invertility; ACF and PACF. MA(1) and MA(2) processes

4.3.3           ARMA models: stationarity and invertibility; ACF and PACF. ARMA(1,1) process

4.4    ARIMA and seasonal ARIMA models

4.4.1           Models for non stationary time series; ARIMA(p,q) models

4.4.2           Modeling seasonality: ARIMA(p,d,q)(P,D,Q)s models

4.5    Model building

4.5.1           Model identification: producing stationarity; using sample ACF and PACF to choose a model

4.5.2           Model   estimation: notes on estimation methods; parameter evaluation

4.5.3           Model diagnostics: tests on residuals