QUANTITATIVE METHODS

Quantitative Methods



Executive summary

Quaterly House sales Data for period from the beginning of 1997 until the middle of 2005 were analyzed by time-series methods. Autocorrelation and partial autocorrelation functions were calculated for the data. Appropriate Box-Jenkins autoregressive integrated moving average model was fitted. Validity of the model was tested using standard statistical techniques. The forecasting power of autoregressive integrated moving average model was used to forecast house sales for three leading years.

Sales are the lifeblood of a business. It's what helps businesses to pay employees, cover operating expenses, buy more inventory, market new products and attract more investors. Sales forecasting is a crucial part of the financial planning of a business. It's a self-assessment tool that uses past and current sales statistics to intelligently predict future performance.

With an accurate sales forecast in hand, organization can plan for the future. If sales forecast says that during December organisation make 30 percent of yearly sales, then they need to ramp up manufacturing in September to prepare for the rush. It might also be smart to invest in more seasonal salespeople and start a targeted marketing campaign right after Thanksgiving. One simple sales forecast can inform every other aspect of your business.

Sales forecasts are also an important part of starting a new business. Almost all new businesses need loans or start-up capital to purchase everything necessary to get off the ground: office space, equipment, inventory, employee salaries and marketing.

Table of content

EXECUTIVE SUMMARY2

INTRODUCTION5

Aim and objective5

DISCUSSION6

Theoretical Basis of Time-Series Analysis:7

Building ARIMA model for Total houses sold per quarter data and Forecasting:14

Model identification:15

Model estimation and verification:15

Model 1: ARIMA (1, 1, 1)16

Model 2: AR(1)19

Model 3: ARIMA(0,1,0)(1,1,0)23

Model 4: MA (1)26

Model 5: ARIMA (2, 1, 1)29

Model 6: ARIMA (1, 1, 2)32

Model 7: ARIMA (2, 1, 0)34

Model 8: ARIMA (2, 1, 1)37

Models and corresponding AIC41

CONCLUSION41

Recommendation42

REFERENCES43

APPENDIX44

Quantitative Methods

Introduction

As the world's economy is going through some very difficult times, governments and businesses around the world find it ever more important to have accurate assessments of the future. This will enable them to do their planning and will facilitate better decision making. This project involves a large company which deals with real estate. The management of the company wants to arrive at an accurate low in complexity inexpensive and time-saving forecasting model that could be used to predict sales of houses for a particular area of a large city.

Aim and objective

The aim of this project is to apply appropriate time series forecasting methods in order to help the management of the company to choose an appropriate forecasting model that could be used to predict house sales in the short term with a reasonable level of accuracy. The company has provided quarterly data which covers the period from the beginning of 1997 until the middle of 2005. The requirements of work are specified in the next section.

Discussion

Autoregressive Integrated Moving Average (ARIMA) model was introduced by Box and Jenkins (hence also known as Box-Jenkins model) in 1960s for forecasting a variable. An effort is made in this paper to develop an ARIMA model ...