Annual temperature analysis using - Time series

parc

Could someone tell me the the steps needed to analyse a time series graph of a deuterium and temperature relationship over a few thousand years (from an ice core) and what are the characteristically I should examine. (See italics for an explanation)

How should I examine this data


Thanks

If there's lots of deuterium, this means that the temperature at that time of year was high (as deuterium molecues are heavy, it takes a great deal of heat to make them evaporate, indicating that it was a warm year

bnt

The first thing I would do is check for statistical Correlation. In Excel you have the CORREL function that does this: it takes two series of values and returns a number between -1 (negative correlation) and +1 (positive correlation). If you get zero, the numbers may as well be random, since that indicates no correlation either way, but if you get > 0.5 you might be on to something.

parc

Cool thanks a lot

Just one more question about regression lines. What are they for?

In the picture below would the top graph indicate a positive relationship and the bottom indicate a negative one?

hivizman

parc wrote: »

Cool thanks a lot

Just one more question about regression lines. What are they for?

A regression line is sometimes called the "line of best fit" - it assumes that there is a linear relationship between two variables of the form:

y = a +b.x

Here, y is the dependent variable and x is the independent (explanatory) variable. a is the intercept and b is the coefficient on x.

There are various techniques for estimating the line of best fit, some of which are discussed in the Wikipedia article on linear regression.

parc wrote: »

In the picture below would the top graph indicate a positive relationship and the bottom indicate a negative one?

The top diagram clearly suggests a positive relationship (variable y increases as variable x increases). The points are clustered closely around the regression line, suggesting a close relationship between the two variables and a significantly positive correlation coefficient.

The bottom diagram suggests a negative relationship (variable y decreases as variable x increases). However, the shape of the distribution of points suggests to me a non-linear relationship. In this case, using linear regression on the raw data is likely to lead to what statisticians call "model mis-specification". If I got this sort of scatter diagram, I'd probably transform the y variable - I'd first of all investigate what happens if I use log(y) (logarithmic transformation) instead of y as the dependent variable in the regression, and then I'd try sqrt(y) (square root transformation).

By the way, if your data represent two time series, using linear regression can produce spurious correlations, and it is considered better to use more advanced techniques such as testing for cointegration.

bnt

As hivizman says, a linear regression line assumes a linear relationship in the data. It's generated using a mathematical formula, and will give you a line through any data set, even random data. So the fact that you can draw a line isn't meaningful in itself, but you can calculate a measure of its "goodness of fit", usually called a "R-squared" value.

If you add a regression line to an Excel chart, you have the option to display the line's formula and a R-squared value. You can even try different regression types (linear or non-linear) and look for the best R-squared value: a quick-and-dirty method of determining the type of relationship, if any, that you might find in the data.

In the case of the first data set, I bet the Excel CORREL function would give you a pretty good positive value (+0.8 or better), while the second data set would show less of a negative correlation (-0.5 or so). But that's because it's a linear function, and the second data set is non-linear in nature i.e. assuming a linear distribution would be wrong.