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 6.39% per annum.
- ABT price at the close of May 20, 2024 was $103.21 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 3.60% per annum.
- ABT price at the close of May 20, 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 12, 2023
a = 4.8904
b = -0.0002
s = 0.0608
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.39%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0608) – 1
= 27.51%
January 25, 2021 calculations
Top border of price channel:
Exp(Y423)
= Exp(a + b × X423 + 2 × s)
= Exp(a + b × 615 + 2 × s)
= Exp(4.8904 + -0.0002 × 615 + 2 × 0.0608)
= Exp(4.9006)
= $134.38
Bottom border of price channel:
Exp(Y423)
= Exp(a + b × X423 – 2 × s)
= Exp(a + b × 615 – 2 × s)
= Exp(4.8904 + -0.0002 × 615 – 2 × 0.0608)
= Exp(4.6576)
= $105.39
December 12, 2023 calculations
Top border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 + 2 × s)
= Exp(a + b × 1,666 + 2 × s)
= Exp(4.8904 + -0.0002 × 1,666 + 2 × 0.0608)
= Exp(4.7105)
= $111.11
Bottom border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 – 2 × s)
= Exp(a + b × 1,666 – 2 × s)
= Exp(4.8904 + -0.0002 × 1,666 – 2 × 0.0608)
= Exp(4.4675)
= $87.14
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.39% per annum.
- ABT price at the close of May 20, 2024 was $103.21 and was inside the primary price channel.
Secondary Trend
Start date: June 10, 2022
End date: May 20, 2024
a = 4.5003
b = 0.0001
s = 0.0554
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.60%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0554) – 1
= 24.83%
June 10, 2022 calculations
Top border of price channel:
Exp(Y771)
= Exp(a + b × X771 + 2 × s)
= Exp(a + b × 1,116 + 2 × s)
= Exp(4.5003 + 0.0001 × 1,116 + 2 × 0.0554)
= Exp(4.7192)
= $112.08
Bottom border of price channel:
Exp(Y771)
= Exp(a + b × X771 – 2 × s)
= Exp(a + b × 1,116 – 2 × s)
= Exp(4.5003 + 0.0001 × 1,116 – 2 × 0.0554)
= Exp(4.4975)
= $89.79
May 20, 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(4.5003 + 0.0001 × 1,826 + 2 × 0.0554)
= Exp(4.7880)
= $120.06
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.5003 + 0.0001 × 1,826 – 2 × 0.0554)
= Exp(4.5662)
= $96.18
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 3.60% per annum.
- ABT price at the close of May 20, 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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