Quantitative Methods I

2010

Time Series Project

Exports, Major Group 4.1 Lumber

By: Justin Landry

Section: 040

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TABLE OF CONTENTS

Page

A. Introduction to Time Series Project ........................................................................................... 3

B. Trend Analysis ...................................................................................................................................... 4

C. Seasonal Variation ............................................................................................................... 5

D. Cyclical and Irregular Variation .................................................................................................. 6

E. Forecast .................................................................................................................................................. 7

F. Discussion and Conclusion .................................................................................................. 8

G. Bibliography ........................................................................................................................................................ 9

H. Appendices and Diagrams ................................................................................ 10

Appendix A: Linear Trend Analysis

Appendix B: Deseasonalization

Appendix C: Cyclical Irregular Indexes

Appendix D: All statistical output data

Appendix E: 8th Year Prediction vs. Actual Data

Appendix F: Total Actual Data vs. Forecasted Data

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A. INTRODUCTION A time series is a method used to analyze and predict future events using past historical

activities, as being aware of those trends can be crucial to the success of business’s,

accuracy is important and in order to have an effective time series analysis there are 4

crucial elements, they are; the Trend Analysis, Seasonal Variation, and Cyclical and Irregular

Variation. The trend analysis is a mathematical technique that uses historical data to predict

future outcomes, and create a forecast for future events. As with any business, there are

seasonal cycles, which is why the Seasonal Variation is a crucial element to the accuracy of

the time series analysis, allowing us to determine what the actual values would have been if

it were not for the seasonal changes. Seasonal Variation is the component which is

dependent on the time of year and it describes any regular fluctuations within a period of

less than a year. We are interested in comparing the seasonal affects within the years, from

year to year. The Cyclical-Irregular variation is used to determine when there irregular

events, causing the actual values to fall either above or below the trend line. The way we

measure the Cyclical-Irregular variation is to calculate the ratio of the actual value (Y) to the

trend value (Yp), and the ratio will determine if we are above or below the expected trend.

In this analysis we will be using data from the export of lumber, a major commodity in

Canada. The model I will be using is the Moving Average Model, which requires a constant

mean. This model also allows for fairly precise information after Moving Average

smoothing, adjusts the errors. The intent of the report is to analyze the trend variations

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from period to period, and to compare a forecast, to the actual statistics, to better

understand the effectiveness of a time series analysis.

B. TREND ANALYSIS Upon completion of a trend-line curve fit (Appendix A) with the assistance of Microsoft

Excel I determined the least-squares trend equation is y = -33.962(x) + 3,021.839. With

this information we now know the slope of the trend line, which thus tell us there is a

difference expected of -33.96$ for every additional X variable, or the forecast for every

additional quarter is 33.96$ less than the previous one. Although, as you can see in

Appendix A, series 1 is the actual values, and the values vary per quarter above or

below the trend line as expected. These differences between the trend and the actual

values are as a result of factors such as the lumber disagreement between Canada and

U.S. or slow construction periods, as a result of economic fluctuations, and many more

influential factors. Also we notice that during the 3rd Quarter of 2002 to the 1st Quarter

of 2004 the exportation of lumber fellow below the expected trend this was due in large

part to American anti-dumping and countervailing duties slapped on the industry from

2002 to 2006, a rise in energy and raw material prices, a decline in lumber prices and a

higher exchange rate for the Canadian dollar. As well on average, prices fell 4.4% a year

from 1999 to 2006. This was the result of several factors including stiffer competition on

international markets, production overcapacity in the industry.

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C. SEASONAL VARIATION After calculating the centered moving average and deseasonalization with the

assistance of Microsoft Excel the following seasonal indexes were determined, for the export of

Lumber in Canada.

Year 1 2 3 4 Total

2001 1.051 0.875 2002 1.028 1.144 0.933 0.970 2003 0.948 0.989 1.043 0.909 2004 0.880 1.162 1.148 0.868 2005 0.953 1.126 0.944 0.946 2006 1.040 1.082 0.979 0.897 2007 0.988 1.155 mean: 0.973 1.110 1.016 0.911 4.010

adjusted: 0.970 1.107 1.014 0.909 4.000

As you can see the two highest quarterly indexes are as expected in the 2nd, and 3rd quarters

overall. This is as a result of a higher demand then the 1st and 4th quarter for the use of lumber.

During the 2nd and 3rd quarters the construction industry becomes very active once the warm

weather begins and as a direct result of that, the greatest export of lumber in Canada is during

the months of Mar- Sept (Q2 and Q3). As well as many other industries such as paper

manufacturer`s would be demanding more lumber in order to meet demands, must be able to

harvest as much lumber to export to paper manufacturer`s even during the slow quarters (Q1 &

Q4). The decline from Q3 2002 to Q3 2003 was as a result of the duties imposed on Canadian

Lumber exporter`s as the cost of lumber continued to decline, but American`s became hesitant

with the potential slow down in the economy and new housing market in 2003. As well the

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steady increase in exportation previously to Q3 2002, was as a result of a grace period where

exporter`s pushed as much of their product to the United States, as there was a grace period

where no duties had to be paid, but as a result of that created a surplus and caused prices to

fall.

D. CYCLICAL AND IRREGULAR VARIATION

Upon review of the chart in Appendix C, it is easily determined that there is a cycle that

does appear to occur over a period of 4 years, but as of recently there has been a steady

decline over the last year. As per the CxI’s in Appendix C there is no clear determinable

cycle, as there have been irregular variations over the last 2 years. Also, when reviewing the

indexes we see that during the slow seasons for the export of lumber that the index fell for

example in Q2 of 2003 to 24 points below expectations. The reason for that decline again

was the end of the softwood lumber agreement, and the implementation of duties on

American importers of Canadian lumber, and a slowing housing market in the Unites States.

The other example of irregular variation is in 2004 Q3, where the index was 33% above

what was predicted. The reason for this increase is the United States, as they have

increased their demand of lumber in 2004 from 67% in 1995, now to 81% of our lumber

export is sent to our neighbours to the south. Also a major reason for why the increase was

so much higher in 2004 was due to Canada exporting 2/3 of all lumber in Canada to other

countries.

E. FORECAST

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After having completed the de-seasonalization analysis, as well as calculating the

seasonal indexes we must now use the formula given in Appendix 2, to calculate a forecast

for the four quarters of 2008, see Appendix D for full calculations.

As you can see above the forecast for the 8th and final year were somewhat above the

actual data. This data is due to irregular variations such as weather and the economy, and

the North American Free Trade agreement as well as the Soft-Wood Lumber Agreement.

Referring to Appendix B the regression equation states r ² = 0.330 which means that there is

a weak relationship between time and the export of lumber, also as part of the regression

analysis performed when conducting our initial trend line, the standard error of estimate is

noted as 405.320, thus giving a more accurate prediction of how much lumber will be

exported for every quarter of 2008. As well should the trend continue the lumber industry

is currently heading towards a possible recession and that a time series analysis is a great

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tool, to predict and plan for situations as such to avoid periods of decreasing GDP in the

lumber sector, which could be detrimental to Canada’s economy as lumber is a major

contributor to the net export calculation of GDP.

F. DISCUSSION AND CONCLUSION

After completing all calculations we can determine that the forecasted predictions are

somewhat accurate, but there are some discrepancies due to a lot of fluctuations in the

demand from our major consumer, the United States. In terms of accuracy when using the

deseasonalized data and the standard of error, your predictions become much more precise

once you take into consideration and the forecast becomes much more accurate.

In conclusion, the time series analysis is a very useful tool, but can sometime be

inaccurate due to irregular actions that take place during the quarter, such as weather, or

the event of a forest fire, which could be detrimental to the lumber industry, should a large

portion of a forest be destroyed. As well it is noticed that the relationship between time and

the export of lumber does not have a positive relationship, nor does it have a regular

business cycle. Major discrepancies in this analysis, is due mostly in large part to the

seasonal periods as Q2 and Q3, are the busy season for the lumber industry. As well the

Soft-Wood Lumber agreement as well as the duties placed on American importers of

Canadian lumber, which decreased the amount they purchased from us. Overall the Lumber

Industry is still one of the leading industries in Canada, and contributes the majority of net

exports, in the calculation of gross domestic product.

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G. BIBLIOGRAPHY

Canada, S. (2010). CANISM Merchandise imports and exports, by major groups and principal trading areas for all countries, quarterly (dollars). Retrieved 2010, from Statistics Canada: http://estat.statcan.gc.ca/cgi-win/cnsmcgi.exe?Lang=E&EST-Fi=EStat/English/CII_1-eng.htm

Canada, S. (n.d.). Export trade vital to the lumber industry. Retrieved 2010, from Statistics Canada.

Lind, M. W. Basic Statistics for Business & Economics (Vol. Third Canadian Edition). McGrawHill.

Schrier, D. (2002, December). BC Stats. Retrieved April 4, 2010, from bcstats.gov.bc.ca: http://www.bcstats.gov.bc.ca/pubs/exp/exp0210.pdf

The Canadian Lumber Industry: Recent Trends. (2003). Retrieved 2010, from Statistics Canada: http://www.statcan.gc.ca/pub/11-621-m/11-621-m2007055-eng.htm

Time Series Analysis. (n.d.). Retrieved 2010, from Stat Soft Electronic Statistics Textbook: http://www.statsoft.com/textbook/time-series-analysis/#two

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H. APPENDICES AND DIAGRAMS Appendix A Trend Line

Appendix B

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Appendix C. Cyclical-Irregular Indexes

Appendix D

Year Quarter X

Value Data

Predicted Y (Yp)

Seasonal

Trend Line

2001

I 1 2553.1 2969.176 2987.877

II 2 3386.3 2936.352 2953.915

III 3 3131.3 2903.528 2919.953

IV 4 2632.6 2870.704 2885.991

2002

I 5 2980.2 2837.88 2852.029

II 6 3185.1 2805.056 2818.067

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III 7 2475.8 2772.232 2784.105

IV 8 2365.1 2739.408 2750.143

2003

I 9 2192.1 2706.584 2716.181

II 10 2259.7 2673.76 2682.219

III 11 2390.3 2640.936 2648.257

IV 12 2228.2 2608.112 2614.295

2004

I 13 2387.3 2575.288 2580.333

II 14 3345.2 2542.464 2546.371

III 15 3387.7 2509.64 2512.409

IV 16 2552.9 2476.816 2478.447

2005

I 17 2653.2 2443.992 2444.485

II 18 2991 2411.168 2410.523

III 19 2486.2 2378.344 2376.561

IV 20 2437.1 2345.52 2342.599

2006

I 21 2591.6 2312.696 2308.637

II 22 2591.4 2279.872 2274.675

III 23 2213.7 2247.048 2240.713

IV 24 1926.8 2214.224 2206.751

2007

I 25 2035.6 2181.4 2172.789

II 26 2243.1 2148.576 2138.827

III 27 1851.6 2115.752 2104.865

IV 28 1348.8 2082.928 2070.903

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2008

I 29 1221.7 2050.104 2036.941

II 30 1507 2017.28 2002.979

III 31 1410 1984.456 1969.017

IV 32 1231.6 1951.632 1935.055

Appendix E

Appendix F