Mathematical modeling for short term indoor room temperature forecasting using Box-Jenkins models
Authors: Pandey Kamal , Basu Bhaskar 
Published: February 2020

Purpose
The rapid urbanization of Indian cities and the population surge in cities has steered a massive demand for energy, thereby increasing the carbon emissions in the environment. Information and technology advancements, aided by predictive tools, can optimize this energy demand and help reduce harmful carbon emissions. Out of the multiple factors governing the energy consumption and comfort of buildings, indoor room temperature is a critical one, as it envisages the need for regulating the temperature. This paper aims to propose a mathematical model for short-term forecasting of indoor room temperature in the Indian context to optimize energy consumption and reduce carbon emissions in the environment.

Design/methodology/approach
A study is conducted to forecast the indoor room temperature of an Indian corporate building structure, based upon various external environmental factors: temperature and rainfall and internal factors like cooling control, occupancy behavior and building characteristics. Expert insight and principal component analysis are applied for appropriate variables selection. The machine learning approach using Box–Jenkins time series models is used for the forecasting of indoor room temperature.

Findings
ARIMAX model, with lagged forecasted and explanatory variables, is found to be the best-fit model. A predictive short-term hourly temperature forecasting model is developed based upon ARIMAX model, which yields fairly accurate results for data set pertaining to the building conditions and climatic parameters in the Indian context. Results also investigate the relationships between the forecasted and individual explanatory variables, which are validated using theoretical proofs.

Research limitations/implications
The models considered in this research are Box–Jenkins models, which are linear time series models. There are non-linear models, such as artificial neural network models and deep learning models, which can be a part of this study. The study of hybrid models including combined forecasting techniques comprising linear and non-linear methods is another important area for future scope of study. As this study is based on a single corporate entity, the models developed need to be tested further for robustness and reliability.

Practical implications
Forecasting of indoor room temperature provides essential practical information about meeting the in-future energy demand, that is, how much energy resources would be needed to maintain the equilibrium between energy consumption and building comfort. In addition, this forecast provides information about the prospective peak usage of air-conditioning controls within the building indoor control management system through a feedback control loop. The resultant model developed can be adopted for smart buildings within Indian context.

Social implications
This study has been conducted in India, which has seen a rapid surge in population growth and urbanization. Being a developing country, India needs to channelize its energy needs judiciously by minimizing the energy wastage and reducing carbon emissions. This study proposes certain pre-emptive measures that help in minimizing the consumption of available energy resources as well as reducing carbon emissions that have significant impact on the society and environment at large.

Originality/value
A large number of factors affecting the indoor room temperature present a research challenge for model building. The paper statistically identifies the parameters influencing the indoor room temperature forecasting and their relationship with the forecasted model. Considering Indian climatic, geographical and building structure conditions, the paper presents a systematic mathematical model to forecast hourly indoor room temperature for next 120 h with fair degree of accuracy.