by Timothy L. McMurry and Dimitris N. Politis.

*Foresight* (Fall, 2014). pp.42-48.

This is an introduction to our approach to forecast reconciliation without using any matrices. The original research is available here:

The software is available in the hts package for R with some notes on usage in the vignette. There is also a gentle introduction in my forecasting textbook.

]]>**Venue**: The University Club, University of Western Australia, Nedlands WA.

**Requirements:** a laptop with R installed, along with the fpp package and its dependencies. We will also use the hts and vars package on the third day.

Hyndman and Athanasopoulos (2014)

*Forecasting: principles and practice*,

OTexts: Melbourne, Australia.

- Introduction to forecasting [Slides, R code, Lab solutions]
- Forecasting tools [Slides, R code, Lab solutions]
- Exponential smoothing I [Slides, R code, Lab solutions]
- Exponential smoothing II [Slides, R code, Lab solutions]
- Time series decomposition and cross-validation [Slides, R code, Lab solutions]
- Transformations, stationarity and differencing [Slides, R code, Lab solutions]
- Non-seasonal ARIMA models [Slides, R code, Lab solutions]
- Seasonal ARIMA models [Slides, R code, Lab solutions]
- State space models [Slides, R code, Lab solutions]
- Dynamic regression [Slides, R code, Lab solutions]
- Hierarchical forecasting [Slides, R code, Lab solutions]
- Advanced methods [Slides, R code, Lab solutions]

**Venue:** LvB Library, Room 401, Spandauerstr. 1, 10178 Berlin

**Time:**

24 June 2014, 09:30 – 12:30 and 14:00 – 17:00

25 June 2014, 09:30 – 11:30

**Abstract:**

Functional time series are curves that are observed sequentially in time, one curve being observed in each time period. In demography, examples include curves formed by annual death rates as a function of age, or annual fertility rates as a function of age. In finance, functional time series can occur in the form of bond yield curves, for example, with each curve being the yield of a bond as a function of the maturity of a bond.

I will discuss methods for describing, modelling and forecasting such functional time series data. Challenges include:

- developing useful graphical tools (I will illustrate a functional version of the boxplot);
- dealing with outliers (e.g., death rates have outliers in years of wars or epidemics);
- cohort effects (how can we identify and allow for these in the forecasts);
- synergy between groups (e.g, we expect male and female mortality rates to evolve in a similar way in the future, and we expect different types of yield curves to behave similarly over time);
- deriving prediction intervals for forecasts;
- how to combine mortality and fertility forecasts to obtain forecasts of the total population;
- how to use these ideas to simulate the age-structure of future populations and use the results to analyse proposed government policies.

**Lectures:**

- Tools for functional time series analysis [Slides]
- Automatic time series forecasting [Slides]
- Forecasting functional time series [Slides]
- Connections, extensions and applications [Slides]
- Forecasting functional time series via PLS [Slides]
- Coherent functional forecasting [Slides]
- Common functional principal components [Slides]
- Stochastic population forecasting [Slides]

**Abstract: **Electricity demand forecasting plays an important role in short-term load allocation and long-term planning for future generation facilities and transmission augmentation. It is a challenging problem because of the different uncertainties including underlying population growth, changing technology, economic conditions, prevailing weather conditions (and the timing of those conditions), as well as the general randomness inherent in individual usage. It is also subject to some known calendar effects due to the time of day, day of week, time of year, and public holidays. But the most challenging part is that we often want to forecast the peak demand rather than the average demand. Consequently, it is necessary to adopt a probabilistic view of potential peak demand levels in order to evaluate and hedge the financial risk accrued by demand variability and forecasting uncertainty.

**Part 1:** I will describe some Australian experiences in addressing these problems, and a comprehensive forecasting solution designed to take all the available information into account, and to provide forecast distributions from a few hours ahead to a few decades ahead. The approach is being used by energy market operators and supply companies to forecast the probability distribution of electricity demand in various regions of Australia.

Slides (part 1). Handout

**Part 2:** I will also discuss some recent developments in evaluating peak demand forecasts, and some research competitions that have generated some innovative new methods to tackle energy forecasting problems.

Slides (part 2). Handout

Department of Econometrics & Business Statistics, Monash University, Australia

**Abstract:** We propose a new generic method ROPES (Regularized Optimization for Prediction and Estimation with Sparse data) for decomposing, smoothing and forecasting two-dimensional sparse data. In some ways, ROPES is similar to Ridge Regression, the LASSO, Principal Component Analysis (PCA) and Maximum-Margin Matrix Factorisation (MMMF). Using this new approach, we propose a practical method of forecasting mortality rates, as well as a new method for interpolating and extrapolating sparse longitudinal data. We also show how to calculate prediction intervals for the resulting estimates.

- Department of Econometrics and Business Statistics, Monash University, Australia
- University of Auckland, New Zealand.

**Abstract**

We describe some fast algorithms for reconciling large collections of time series forecasts with aggregation constraints. The constraints arise due to the need for forecasts of collections of time series with hierarchical or grouped structures to add up in the same manner as the observed time series. We show that the least squares approach to reconciling hierarchical forecasts can be extended to more general non-hierarchical groups of time series, and that the computations can be handled efficiently by exploiting the structure of the associated design matrix. Our algorithms will reconcile hierarchical forecasts with hierarchies of unlimited size, making forecast reconciliation feasible in business applications involving very large numbers of time series.

**Keywords**: combining forecasts; grouped time series; hierarchical time series; reconciling forecasts; weighted least squares.

- Exponential smoothing
- Structural models
- ARIMA and RegARMA models, and dlm

*(Updated: 2 June 2014)*

International Workshop on Functional and Operatorial Statistics, Stresa, Italy. 19-21 June 2014

- Monash University, Australia.
- University of Karachi, Pakistan.

**Abstract:** We explore models for forecasting groups of functional time series data that exploit common features in the data. Our models involve fitting common (or partially common) functional principal component models and forecasting the coefficients using univariate time series methods. We illustrate our approach by forecasting age-specific mortality rates for males and females in Australia.