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 16.09% per annum.
- ZTS price at the close of April 26, 2024 was $158.42 and was higher than the top border of the primary price channel by $9.71 (6.53%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 11.14% per annum.
- ZTS price at the close of April 26, 2024 was lower than the bottom border of the secondary price channel by $5.67 (3.46%). This indicates a possible reversal in the secondary trend direction.
- 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 ZTS 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: May 20, 2021
End date: April 5, 2023
a = 5.6994
b = -0.0005
s = 0.0895
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0005) – 1
= -16.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0895) – 1
= 43.02%
May 20, 2021 calculations
Top border of price channel:
Exp(Y520)
= Exp(a + b × X520 + 2 × s)
= Exp(a + b × 752 + 2 × s)
= Exp(5.6994 + -0.0005 × 752 + 2 × 0.0895)
= Exp(5.5170)
= $248.90
Bottom border of price channel:
Exp(Y520)
= Exp(a + b × X520 – 2 × s)
= Exp(a + b × 752 – 2 × s)
= Exp(5.6994 + -0.0005 × 752 – 2 × 0.0895)
= Exp(5.1592)
= $174.03
April 5, 2023 calculations
Top border of price channel:
Exp(Y992)
= Exp(a + b × X992 + 2 × s)
= Exp(a + b × 1,437 + 2 × s)
= Exp(5.6994 + -0.0005 × 1,437 + 2 × 0.0895)
= Exp(5.1879)
= $179.10
Bottom border of price channel:
Exp(Y992)
= Exp(a + b × X992 – 2 × s)
= Exp(a + b × 1,437 – 2 × s)
= Exp(5.6994 + -0.0005 × 1,437 – 2 × 0.0895)
= Exp(4.8301)
= $125.22
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 16.09% per annum.
- ZTS price at the close of April 26, 2024 was $158.42 and was higher than the top border of the primary price channel by $9.71 (6.53%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 5, 2022
End date: March 20, 2024
a = 4.7071
b = 0.0003
s = 0.0672
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 11.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0672) – 1
= 30.85%
May 5, 2022 calculations
Top border of price channel:
Exp(Y762)
= Exp(a + b × X762 + 2 × s)
= Exp(a + b × 1,102 + 2 × s)
= Exp(4.7071 + 0.0003 × 1,102 + 2 × 0.0672)
= Exp(5.1604)
= $174.24
Bottom border of price channel:
Exp(Y762)
= Exp(a + b × X762 – 2 × s)
= Exp(a + b × 1,102 – 2 × s)
= Exp(4.7071 + 0.0003 × 1,102 – 2 × 0.0672)
= Exp(4.8915)
= $133.16
March 20, 2024 calculations
Top border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 + 2 × s)
= Exp(a + b × 1,787 + 2 × s)
= Exp(4.7071 + 0.0003 × 1,787 + 2 × 0.0672)
= Exp(5.3586)
= $212.43
Bottom border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 – 2 × s)
= Exp(a + b × 1,787 – 2 × s)
= Exp(4.7071 + 0.0003 × 1,787 – 2 × 0.0672)
= Exp(5.0897)
= $162.35
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 11.14% per annum.
- ZTS price at the close of April 26, 2024 was lower than the bottom border of the secondary price channel by $5.67 (3.46%). This indicates a possible reversal in the secondary trend direction.
- 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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