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 January 17, 2025 was $113.48 and was higher than the top border of the primary price channel by $11.54 (11.32%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.19% per annum.
- ABT price at the close of January 17, 2025 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 = 4.8283
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(Y252)
= Exp(a + b × X252 + 2 × s)
= Exp(a + b × 365 + 2 × s)
= Exp(4.8283 + -0.0002 × 365 + 2 × 0.0610)
= Exp(4.8851)
= $132.31
Bottom border of price channel:
Exp(Y252)
= Exp(a + b × X252 – 2 × s)
= Exp(a + b × 365 – 2 × s)
= Exp(4.8283 + -0.0002 × 365 – 2 × 0.0610)
= Exp(4.6410)
= $103.65
December 11, 2023 calculations
Top border of price channel:
Exp(Y980)
= Exp(a + b × X980 + 2 × s)
= Exp(a + b × 1,420 + 2 × s)
= Exp(4.8283 + -0.0002 × 1,420 + 2 × 0.0610)
= Exp(4.6964)
= $109.55
Bottom border of price channel:
Exp(Y980)
= Exp(a + b × X980 – 2 × s)
= Exp(a + b × 1,420 – 2 × s)
= Exp(4.8283 + -0.0002 × 1,420 – 2 × 0.0610)
= Exp(4.4523)
= $85.83
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.32% per annum.
- ABT price at the close of January 17, 2025 was $113.48 and was higher than the top border of the primary price channel by $11.54 (11.32%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: June 10, 2022
End date: January 17, 2025
a = 4.4594
b = 0.0001
s = 0.0533
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0533) – 1
= 23.75%
June 10, 2022 calculations
Top border of price channel:
Exp(Y603)
= Exp(a + b × X603 + 2 × s)
= Exp(a + b × 871 + 2 × s)
= Exp(4.4594 + 0.0001 × 871 + 2 × 0.0533)
= Exp(4.6868)
= $108.50
Bottom border of price channel:
Exp(Y603)
= Exp(a + b × X603 – 2 × s)
= Exp(a + b × 871 – 2 × s)
= Exp(4.4594 + 0.0001 × 871 – 2 × 0.0533)
= Exp(4.4737)
= $87.68
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.4594 + 0.0001 × 1,823 + 2 × 0.0533)
= Exp(4.8188)
= $123.82
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.4594 + 0.0001 × 1,823 – 2 × 0.0533)
= Exp(4.6057)
= $100.06
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.19% per annum.
- ABT price at the close of January 17, 2025 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.
Check out ABT and 1,499 other stocks on our new website