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Probabilistic Modelling for Hierarchical Time Series Forecasting

IP.com Disclosure Number: IPCOM000239722D
Publication Date: 2014-Nov-27

Publishing Venue

The IP.com Prior Art Database

Related People

Chris Yan: INVENTOR [+2]

Abstract

A method is disclosed for probabilistic modelling for hierarchical time series forecasting. The method combines an individual forecast model that includes the state space model with an efficient probabilistic model by either solving a close form equation or running Markov Chain Monte Carlo (MCMC) sampling based on different assumptions. The method, then, provides forecasting results that achieve a high level of accuracy for each node and consistency for a hierarchical structure.

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Probabilistic Modelling for Hierarchical Time Series Forecasting

Abstract

A method is disclosed for probabilistic modelling for hierarchical time series forecasting.  The method combines an individual forecast model that includes the state space model with an efficient probabilistic model by either solving a close form equation or running Markov Chain Monte Carlo (MCMC) sampling based on different assumptions.  The method, then, provides forecasting results that achieve a high level of accuracy for each node and consistency for a hierarchical structure.

Description

Time series forecasting is very important for internet industry.  It provides critical information for businesses, such as, but not limited to, traffic of page views, user visits and search volume, to support corporate planning.  Yet, due to the complicated infrastructure, accurate forecasting is very challenging.  The huge volume of traffic data is typically organized in a hierarchical tree structure.  The typical hierarchical tree structure can be a parent node as an aggregation of its child nodes.  Therefore, forecasting should not only focus on accuracy for each individual node but also maintain the consistency between the parent nodes and child nodes.

Disclosed is a method for probabilistic modelling for hierarchical time series forecasting.  The method combines an individual forecast model that includes the state space model with an efficient probabilistic model by either solving a close form equation or running Markov Chain Monte Carlo (MCMC) sampling based on different assumptions.  The method, then, provides forecasting results that achieve a high level of accuracy for one or more nodes and consistency for a hierarchical structure.

In an embodiment, the method represents each time series as a vector parameterized by time as,

: .

Without confusion, the method frequently drops time t indices when describing hierarchical relations between different nodes.  The method uses foot indices to represent time series from different nodes in the hierarchical tree.

Consider a very typical hierarchy structure as

,

which means that parent node  is constructed as the summation of all descendent nodes from  to .  The method indicates the forecast for each corresponding node as: .  Noting that forecast  and  may or may not fit the summation constraint since each one comes from individual forecasting models and summation constraint is not explicitly mentioned in the step above.

Considering a specific time point t, the method defines

.

Ideally if forecast is 100% accurate,  should be 0.  In reality, the method models the density function of such error following a Gaussian distribution with mean  and variance .  Then the joint distribution at time t for all s in the hierarchy would be:

.

Considering an independence assumption between different noises holds as a degraded case, the joint probability density could be written as the product of a group of Gaussian distributions:...