Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 58.27% per annum.
- IBM price at the close of March 27, 2024 was $190.80 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 113.45% per annum.
- IBM price at the close of March 27, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of IBM price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: April 13, 2023
End date: March 27, 2024
a = 2.9342
b = 0.0013
s = 0.0419
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 58.27%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0419) – 1
= 18.25%
April 13, 2023 calculations
Top border of price channel:
Exp(Y1,018)
= Exp(a + b × X1,018 + 2 × s)
= Exp(a + b × 1,477 + 2 × s)
= Exp(2.9342 + 0.0013 × 1,477 + 2 × 0.0419)
= Exp(4.8759)
= $131.09
Bottom border of price channel:
Exp(Y1,018)
= Exp(a + b × X1,018 – 2 × s)
= Exp(a + b × 1,477 – 2 × s)
= Exp(2.9342 + 0.0013 × 1,477 – 2 × 0.0419)
= Exp(4.7082)
= $110.85
March 27, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.9342 + 0.0013 × 1,826 + 2 × 0.0419)
= Exp(5.3149)
= $203.33
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.9342 + 0.0013 × 1,826 – 2 × 0.0419)
= Exp(5.1472)
= $171.95
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 58.27% per annum.
- IBM price at the close of March 27, 2024 was $190.80 and was inside the primary price channel.
Secondary Trend
Start date: September 29, 2023
End date: March 27, 2024
a = 1.4997
b = 0.0021
s = 0.0272
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 113.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0272) – 1
= 11.49%
September 29, 2023 calculations
Top border of price channel:
Exp(Y1,135)
= Exp(a + b × X1,135 + 2 × s)
= Exp(a + b × 1,646 + 2 × s)
= Exp(1.4997 + 0.0021 × 1,646 + 2 × 0.0272)
= Exp(4.9734)
= $144.52
Bottom border of price channel:
Exp(Y1,135)
= Exp(a + b × X1,135 – 2 × s)
= Exp(a + b × 1,646 – 2 × s)
= Exp(1.4997 + 0.0021 × 1,646 – 2 × 0.0272)
= Exp(4.8647)
= $129.63
March 27, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.4997 + 0.0021 × 1,826 + 2 × 0.0272)
= Exp(5.3473)
= $210.05
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.4997 + 0.0021 × 1,826 – 2 × 0.0272)
= Exp(5.2386)
= $188.41
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 113.45% per annum.
- IBM price at the close of March 27, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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