Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.37% per annum.
- ABT price at the close of April 24, 2024 was $106.89 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 3.88% per annum.
- ABT price at the close of April 24, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 ABT 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: January 25, 2021
End date: December 13, 2023
a = 4.8945
b = -0.0002
s = 0.0608
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.37%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0608) – 1
= 27.52%
January 25, 2021 calculations
Top border of price channel:
Exp(Y441)
= Exp(a + b × X441 + 2 × s)
= Exp(a + b × 641 + 2 × s)
= Exp(4.8945 + -0.0002 × 641 + 2 × 0.0608)
= Exp(4.9005)
= $134.35
Bottom border of price channel:
Exp(Y441)
= Exp(a + b × X441 – 2 × s)
= Exp(a + b × 641 – 2 × s)
= Exp(4.8945 + -0.0002 × 641 – 2 × 0.0608)
= Exp(4.6574)
= $105.36
December 13, 2023 calculations
Top border of price channel:
Exp(Y1,168)
= Exp(a + b × X1,168 + 2 × s)
= Exp(a + b × 1,693 + 2 × s)
= Exp(4.8945 + -0.0002 × 1,693 + 2 × 0.0608)
= Exp(4.7108)
= $111.14
Bottom border of price channel:
Exp(Y1,168)
= Exp(a + b × X1,168 – 2 × s)
= Exp(a + b × 1,693 – 2 × s)
= Exp(4.8945 + -0.0002 × 1,693 – 2 × 0.0608)
= Exp(4.4677)
= $87.16
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.37% per annum.
- ABT price at the close of April 24, 2024 was $106.89 and was inside the primary price channel.
Secondary Trend
Start date: June 13, 2022
End date: April 24, 2024
a = 4.4875
b = 0.0001
s = 0.0563
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.88%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0563) – 1
= 25.27%
June 13, 2022 calculations
Top border of price channel:
Exp(Y790)
= Exp(a + b × X790 + 2 × s)
= Exp(a + b × 1,145 + 2 × s)
= Exp(4.4875 + 0.0001 × 1,145 + 2 × 0.0563)
= Exp(4.7194)
= $112.10
Bottom border of price channel:
Exp(Y790)
= Exp(a + b × X790 – 2 × s)
= Exp(a + b × 1,145 – 2 × s)
= Exp(4.4875 + 0.0001 × 1,145 – 2 × 0.0563)
= Exp(4.4941)
= $89.48
April 24, 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(4.4875 + 0.0001 × 1,826 + 2 × 0.0563)
= Exp(4.7903)
= $120.34
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.4875 + 0.0001 × 1,826 – 2 × 0.0563)
= Exp(4.5650)
= $96.06
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 3.88% per annum.
- ABT price at the close of April 24, 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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