NxTrend - Deterministic trend in a time series

Returns values along a trend curve (e.g., linear, quadratic, exponential, etc.) at time T+m.

Syntax

NxTrend(X, Order, Trend_type, POrder, Const, Horizon, Return_type, $\alpha$)

X

is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Order	Description
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

Trend_type

is the model description flag for the trend function (1 = Linear (default), 2 = Polynomial, 3 = Exponential, 4 = Logarithmic, 5 = Power).

Order	Description
1	Linear (default).
2	Polynomial.
3	Exponential.
4	Logarithmic.
5	Power.

POrder

is the polynomial order. This is only relevant for a polynomial type of trend and is ignored for all others. If missing, POrder = 1.

Const

is the constant or the intercept value to fix (e.g., zero). If missing, an intercept will not be fixed and is computed normally.

Horizon

is the forecast time/horizon beyond the end of X. If missing, a default value of 0 (latest or end of X) is assumed.

Return_type

is a switch to select the return output (1 = Forecast value (default), 2 = Upper limit, 3 = Lower Limit, 4 = R-Squared).

Method	Description
1	Forecast value (default).
2	C.I. upper limit.
3	C.I. lower limit.
4	R-Squared.

$\alpha$

is the statistical significance or confidence level (i.e., alpha). If missing or omitted, an alpha value of 5% is assumed.

Remarks

1. NxTrend supports the following trend functions:
   $$ \begin{cases} \mathrm{Linear} & Y_t=\alpha + \beta \times t \\ \mathrm{Polynomial} & Y_t=\alpha + \beta_1 \times t + \beta_2 \times t^2 + \cdots + \beta_N \times t^N \\ \mathrm{Exponential:} & Y_t= \alpha \times e^{\beta \times t} \\ \mathrm{Logarithm:} & Y_t= \alpha + \beta \times \ln(t) \\ \mathrm{Power:} & Y_t= \alpha \times t^{\beta} \\ \end{cases} $$
2. For exponential and logarithmic trends, the intercept value is not permitted to be fixed, and thus is ignored.
3. The Excel trend built-in function (i.e., "TREND") is a different function, not part of NumXL, and should not be confused with NxTrend.
4. The polynomial order argument must be a positive integer.
5. The trend function's coefficients that best fit your data are estimated using the "least squares" method.
6. The time series may include missing values (e.g., #N/A) at either end.

Files Examples

Related Links

• Wikipedia - Least squares regression.

References

• Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.