A trend in a particular time series formally is a prolonged time period wherein X increase or decrease is fast than the average historically. A common approach is used for identifying the time series trending direction which first lies in creating a smooth representation which in a rough manner also describes what X is. The first difference of G can be calculated and the trend then is said to have established within intervals where sign of initial difference has constant rate.
A plot of Oslo Benchmarking index with manual drawn trending lines is provided in the following figure:

The plot is responsible for highlighting an essential barrier that requires to be taken into consideration when a trend has to be selected with mechanism identified. Even the price over the total interval, in general is trending in upward manner; there also are various short term downward trends within the pricing information. Such downtrends in the short term are essential for detecting as we would likely to sell prior to downtrend happens and purchase it again when the uptrend initiates for formation. The trend depicting process however should not be highly sensitive for short term modifications as that can result in false report to break the trend. Therefore, the trend to identify such process needs to have the ability of detecting various trends within a time based series while also not being more sensitive to fluctuations in the short term. In the details that follow, there are 3 possible methods used for calculation of G and for identifying the trends under discussion and evaluation as per the criteria mentioned above.
Regression with simple linearity is a statistics based method to approximate a straightened line by a set of data based points. It is possible for one to assume the straight line presence that describes the data wherein alpha and slope beta can be calculated through use of least estimate squares.

Where alpha dash and beta dash are estimates respectively for alpha and beta. The consequence is a trending line which is responsible for describing the key trend within data. A test for statistical hypothesis can be executed trend for determining if this is an essential data based significant linear relationship.

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