How to calculate general trendline for a time series

[ateixeira]

Hi there,

Given a time series with data points x_1, x_2, x_3,...,x_n I want to be able to extrapolate its future behaviour. I can see three options:

1. \sum_i (x_(i+1)-x_i)/x_i
2. count of how many terms of (x_(i+1)-x_i) are positive and negative
3. Assume linearity and calculate m for the best fit linear aproximation

What I want to know is:

1. Do you think that this makes sense?
2. Do you know of any standardized way to solve this?

Thanks

 

[Stephen Tashi]

[*]Do you think that this makes sense?

No, it doesn't make sense to expect that an answer that can be mathematically justified when so little information about the time series has been given.

[*]Do you know of any standardized way to solve this?

You can find many references on "time series analysis". They won't solve your problem as you have stated it since the statement doesn't give enough information. However, if you look up material on time series analysis it will show you the type of assumptions or facts that must be given in order for various prediction methods to work.

 

[ateixeira]

Thanks for your reply Stephen and sorry for not being specific enough.

No, it doesn't make sense to expect that an answer that can be mathematically justified when so little information about the time series has been given.

In that case let us assume that I'm analyzing the sales of a given product on given time frame (say 6 months).

What I want to be able to do is:

1. understand if the sales are experiencing an upward or downward tendency
2. Predict the next data point

 

[Stephen Tashi]

In that case let us assume that I'm analyzing the sales of a given product on given time frame (say 6 months).

That is still not enough mathematical information about the problem. For example, the sales of products like sun tan lotion may depend on the season or the weather. If you don't understand mathematical modeling, I suggest that you just do a linear regression (i.e. a linear curve fit). Or post a plot of the data and I'm sure someone will chime-in with an opinion about what kind of curve fits it.

 

[CellCoree]

,

I would first like to clarify that there is no one "correct" way to calculate a trendline for a time series. Different methods may be appropriate depending on the specific data and the goals of the analysis. However, there are some common approaches that are often used in scientific research.

The first method you mentioned, calculating the sum of changes in the data and dividing by the initial value, is known as the compound annual growth rate (CAGR). This can be a useful measure for determining the average rate of change over a period of time, but it may not accurately capture short-term fluctuations in the data.

The second method, counting the number of positive and negative changes, can give a general sense of the direction of the trend, but it does not take into account the magnitude of the changes.

The third method, assuming linearity and finding the best fit linear approximation, is a common approach in statistical analysis. This involves using a regression model to find the line that best fits the data and using the slope of that line as the trendline.

In terms of a standardized way to calculate a trendline, there are a few options. One is to use statistical software such as Excel or R to perform a regression analysis and find the best fit line. Another option is to use a time series forecasting method such as exponential smoothing or ARIMA modeling, which take into account trends and patterns in the data to make predictions about future behavior.

In conclusion, there are multiple ways to calculate a trendline for a time series, and the best approach will depend on the specific data and goals of the analysis. It is important to carefully consider the strengths and limitations of each method before making any conclusions about the trend in the data.