Time Series Analysis

What’s it all about?

A technique in Budgeting that allows us to determine the amount and timing of future sales (and the production needed) based on an analysis of past sales. Mostly used where there is seasonality in sales.

Issues in seasonal sales.

Seasonality is very important in some industries. having all of your production/sales at one time of year can be very risky for a company and they will try to balance this out across their products.

Christmas cards are very seasonal, but card shops don’t just sell Christmas cards. You can buy the obvious like birthday cards which should sell equally all year round, but the card industry has attempted to have other seasonal sales to try and boost sales overall. Cards for Mothers’ Day, Valentines Day, all hae a history of being promoted by the card manufacturers to boost their sales. Take a look next time you are in a card shop.

How about this for seasonality, Canadian Resort Hotels expect 100% occupancy in the summer and 5% occupancy in the winter. How do you cope with that sort of cash flow? (from an ‘Undercover Boss: Canada’ programme).

Using Time Series Analysis, we expect to be able to calculate the likely proportion of annual sales that will happen in a particular season. If we also have a prediction of total sales in the next year, we can predict how many of them should happen in each period.

Most, but not all, school wear sales tend to happen in the summer holiday months. did you hate seeing all the ‘Back to School’ adverts as soon as you were on holiday? Six weeks holiday was just not enough.

So that’s one type of seasonality, and to a certain extent we can predict it and plan for it.

School Uniform sales are a very seasonal product with the vast majority being sold in the run up to the start of the new school year. Interesting when it is referred to as a boost for retail sales when surely it is anticipated? We know when kids go back to school and it happens every year. It probably reflects poor sales at other times if something predictable is seen as a boost.

“UK retail sales rose in August helped by small shops enjoying a boost from school uniform buying..”


Watch this.


Christmas Adverts are clearly for seasonal products, but I was surprised to see an advert for batteries. Mind you, I guess with all the products sold ‘batteries not included’, sales around Christmas must be significant.

Other seasonal factors can come into play though that we cannot predict.

The weather has an impact on sales in addition to/opposition to the expected seasonal trend as this article from 2015 shows. Cool/wet weather reduced sales in August but the same weather encouraged sales in September as autumn clothing lines were sold.

John Lewis fashion sales were up by 17% in the first week of September, after tough trading conditions in August.

Total sales were up by 11% to £86.8m for the week ending September 5, compared with the same period last year.

Barry Matheson, director of retail services, called it “the perfect combination of a damp Bank Holiday Monday, cool weather through the week and a shift in the fall of the calendar for back to school”.


The weather isn’t predictable so we could consider it one of those residual/random variations or we could bear in mind that when we make predictions of seasonal sales that they should really be considered to be part of a range of possibles.

The Addititive Method (the version I teach).

Worked example. Long video as there is a lot to do.

Further Reading.

Seasonal Sales.

One of the main reasons for doing Time Series Analysis is to be able to work out when your sales are likely to be when you have a seasonal product. knowing when your sales are allows you to know when you have to make things/buy things to have them available for sale.

Book Sales

Christmas is an important time for book sales, hence Super Thursday in October when the books expected to be Christmas presents are launched.


Snow Blowers

Here’s an interesting example for a product only used in winter – snow blowers in the USA – note when the company buys them.


Overcoming seasonality in sales.

Wouldn’t it be better if you could sell your product all year round? Ice cream is considered an example of a seasonal product (summer obviously). The bigger brands often advertise out of season to encourage sales all year round.

Andy Foweather, Sales Director, General Mills UK, says, “Whilst retailers will experience a significant downturn in trade for impulse handheld ice cream during the winter months, it remains a key selling period for luxury ice cream. In fact, 44% of Häagen-Dazs brand sales occur in winter, making it a must stock for retailers all year round.”


Cyclical Effects

Sporting events are a good example of a cyclical impact on sales.

The Rugby World Cup in England 2015 lead to increase in sales. But note the article under Random Events of what happened when England failed to progress.


Economic Cycles.

Economic cycles which run for several years impact on sales – seasonal sales from one year to the next are also affected by economic cycles.

“There is a global economic cycle, with periodic reverses that the policy-makers have to cope with as best they can. It would be great to eliminate the cycle – to end boom and bust – but we can’t and people who say we can end up with egg on their face. All we can do is to try to minimise its amplitude so that it is less destructive of jobs and economic activity more generally, and that is what sensible policy aims to achieve.”


Random Events (Residual).

The fourth element of sales figures, the changes arising from unpredictable events. Seasonal variations are within a year, we expect to sell more holidays in the summer than in March. Cyclical variations affect businesses over a period of years, but are largely predictable. But actually, many of the things that affect industries are Random, just not predictable.

We had a tragic example in 2015. All the analysis of past data going would not be able to predict the sales in the period when a terrorist atrocity affects sales. http://www.independent.co.uk/news/business/news/atrocity-in-tunisia-could-cost-tui-40m-this-year-10455047.html

And then greater impact at home following the Paris murders..


Another example of a residual (random) event that will effect sales. Alton Towers couldn’t predict the problem with the ride, but they know it is going to affect attendances hence the laying off of staff.


Look at the impact of weather here. How predictable would fluctuations in the relative values of currencies be? How could you build either into your predictions of sale for next year?


Other events can be seen as ‘unpredictable’ and have an impact on planning without being disasters.

the launch of a new product or competitor can influence sales. Will potential purchases hold off on buying a Tesla etc. until they see what Dyson has to offer?


Major sporting events have a cyclical effect in that they are held periodically (and at predictable gaps). These cyclical events can be affected by Random events too. The exit of hosts, England from the Rugby World Cup 2015 was predicted to have a huge adverse effect. They really were poor and didn’t deserve to go through. Japan on the other hand were brilliant but despite winning three games didn’t go through. Tragedy!


VW wouldn’t have taken the discovery of their ’emissions errors’ into account when planning their budgets, but it has had a big effect on sales.


Using Time Series Analysis.

Interpreting Trends.

As always you shouldn’t just look at the numbers, you need to consider other aspects, the ‘environment’ affecting the trend that you are looking at.

Here is a fairly clear trend, declining attendance at Catholic church.

I came to this one listening to a radio item about the slowing in decline in Catholic attendance in comparison to other churches. That was data up to 2015, but I’ve only been finding analysis up to a couple of years ago.

Why is there an increase in 2002? Why has the rate of decline reduced?

 Catholic Mass Attendance: 1993-2010

Key Points from the website I got the graph from.

Weekly mass attendance fell between 30.7% between 1993 and 2010, as compared to corresponding falls of 10.9% in the Catholic population and 9.4% in the number of priests over the same period.

In the 50 years between 1912 and 1962, the Catholic Population more than doubled in size. It continued to rise up to 1993, when it peaked at 4.53 million.

Over the same 50 year period, the number of priests also nearly doubled in size, peaking at 7,887 in 1965. The number of priests has fallen each year since 2002. The 2011 total of 5,264 represents the lowest total since 1937.

Why has the decline in attendance slowed?

Among the suggested reasons are:

Pope Benedict XVI visited the UK in September 2010.

Parents attending church to gain the children access to church run schools (though this is likely to be temporary – decline one the last child is in the school – or am I being cynical).

Growth in the population of immigrants many of whom come from Catholic countries in Eastern Europe (and to a lesser extent, Catholic communities in Africa). The major increase in the Catholic population between 1912 and 1962 is attributed to immigration from the Republic of Ireland (and their UK born families).

The ones left are the committed ones (I am not so convinced by this one – won’t old age be reducing the number too).

Similar patterns are shown in other churches.

Why the increase in 2002?  Don’t know.

So what has this got to do with Trend Analysis?

We like accounting to be about simple maths with nice easy answers that explain everything. If this was a graph showing sales of our product we might decide that we were in the stage of the Product Life Cycle where we were in gentle decline – we still have a market, just a smaller one. There would still be money to be made.

However, the ‘market’ could still disappear quite quickly if there were a change in the business environment. Going back to our church attendance numbers – what would happen if the UK left the EEC? Would substantial numbers of our community who are from Eastern Europe leave? What if faith schools had to take pupils without regard to allegiance to their church?

Rule 1. You can’t just read the numbers to make decisions, you need to have an understanding of your business environment.

Rule 2. past performance (here too) is not a guarantee of future performance.

Further reading on this topic:

The table and data above taken from a faith survey at: http://faithsurvey.co.uk/catholics-england-and-wales.html. You can do the survey yourself at http://faithsurvey.co.uk/index.html

Analysis of long-term trends in Church attendance (belief) based on 2011 Census at : http://www.vexen.co.uk/UK/religion.html

BBC news report on church composition from 2010: http://www.bbc.co.uk/news/11297461

Possible Written Questions.

(No indication of marks – the more marks a question gets, the more you are expected to write – detail that is, not just words!) If you can’t answer these, you need to do some more reading. I do ‘find’ questions elsewhere, so these aren’t all questions I have used myself.

 Explain how and why under Time Series Analysis you need to make adjustments to the seasonal variation averages calculated.

What are the advantages of using Time Series Analysis?

What are the potential problems that can arise if you use Time series Analysis to predict sales?