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 6.32% per annum.
- ABT price at the close of November 19, 2024 was $117.13 and was higher than the top border of the primary price channel by $13.57 (13.10%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.71% per annum.
- ABT price at the close of November 19, 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 20, 2021
End date: December 11, 2023
a = 4.8447
b = -0.0002
s = 0.0610
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0610) – 1
= 27.65%
January 20, 2021 calculations
Top border of price channel:
Exp(Y292)
= Exp(a + b × X292 + 2 × s)
= Exp(a + b × 427 + 2 × s)
= Exp(4.8447 + -0.0002 × 427 + 2 × 0.0610)
= Exp(4.8904)
= $133.01
Bottom border of price channel:
Exp(Y292)
= Exp(a + b × X292 – 2 × s)
= Exp(a + b × 427 – 2 × s)
= Exp(4.8447 + -0.0002 × 427 – 2 × 0.0610)
= Exp(4.6463)
= $104.20
December 11, 2023 calculations
Top border of price channel:
Exp(Y1,020)
= Exp(a + b × X1,020 + 2 × s)
= Exp(a + b × 1,482 + 2 × s)
= Exp(4.8447 + -0.0002 × 1,482 + 2 × 0.0610)
= Exp(4.7017)
= $110.14
Bottom border of price channel:
Exp(Y1,020)
= Exp(a + b × X1,020 – 2 × s)
= Exp(a + b × 1,482 – 2 × s)
= Exp(4.8447 + -0.0002 × 1,482 – 2 × 0.0610)
= Exp(4.4576)
= $86.28
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.32% per annum.
- ABT price at the close of November 19, 2024 was $117.13 and was higher than the top border of the primary price channel by $13.57 (13.10%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: June 10, 2022
End date: November 19, 2024
a = 4.4717
b = 0.0001
s = 0.0541
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0541) – 1
= 24.18%
June 10, 2022 calculations
Top border of price channel:
Exp(Y643)
= Exp(a + b × X643 + 2 × s)
= Exp(a + b × 933 + 2 × s)
= Exp(4.4717 + 0.0001 × 933 + 2 × 0.0541)
= Exp(4.6976)
= $109.69
Bottom border of price channel:
Exp(Y643)
= Exp(a + b × X643 – 2 × s)
= Exp(a + b × 933 – 2 × s)
= Exp(4.4717 + 0.0001 × 933 – 2 × 0.0541)
= Exp(4.4811)
= $88.33
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.4717 + 0.0001 × 1,826 + 2 × 0.0541)
= Exp(4.8102)
= $122.76
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.4717 + 0.0001 × 1,826 – 2 × 0.0541)
= Exp(4.5937)
= $98.86
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.71% per annum.
- ABT price at the close of November 19, 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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