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 21.29% per annum.
- ZTS price at the close of May 7, 2024 was $168.45 and was higher than the top border of the primary price channel by $42.06 (33.28%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.72% per annum.
- ZTS price at the close of May 7, 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 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: June 9, 2021
End date: January 20, 2023
a = 5.8770
b = -0.0007
s = 0.0800
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.29%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0800) – 1
= 37.73%
June 9, 2021 calculations
Top border of price channel:
Exp(Y526)
= Exp(a + b × X526 + 2 × s)
= Exp(a + b × 763 + 2 × s)
= Exp(5.8770 + -0.0007 × 763 + 2 × 0.0800)
= Exp(5.5366)
= $253.81
Bottom border of price channel:
Exp(Y526)
= Exp(a + b × X526 – 2 × s)
= Exp(a + b × 763 – 2 × s)
= Exp(5.8770 + -0.0007 × 763 – 2 × 0.0800)
= Exp(5.2165)
= $184.28
January 20, 2023 calculations
Top border of price channel:
Exp(Y933)
= Exp(a + b × X933 + 2 × s)
= Exp(a + b × 1,353 + 2 × s)
= Exp(5.8770 + -0.0007 × 1,353 + 2 × 0.0800)
= Exp(5.1496)
= $172.36
Bottom border of price channel:
Exp(Y933)
= Exp(a + b × X933 – 2 × s)
= Exp(a + b × 1,353 – 2 × s)
= Exp(5.8770 + -0.0007 × 1,353 – 2 × 0.0800)
= Exp(4.8295)
= $125.15
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.29% per annum.
- ZTS price at the close of May 7, 2024 was $168.45 and was higher than the top border of the primary price channel by $42.06 (33.28%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 2, 2022
End date: March 22, 2024
a = 4.7250
b = 0.0003
s = 0.0679
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 10.72%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0679) – 1
= 31.19%
May 2, 2022 calculations
Top border of price channel:
Exp(Y752)
= Exp(a + b × X752 + 2 × s)
= Exp(a + b × 1,090 + 2 × s)
= Exp(4.7250 + 0.0003 × 1,090 + 2 × 0.0679)
= Exp(5.1648)
= $175.00
Bottom border of price channel:
Exp(Y752)
= Exp(a + b × X752 – 2 × s)
= Exp(a + b × 1,090 – 2 × s)
= Exp(4.7250 + 0.0003 × 1,090 – 2 × 0.0679)
= Exp(4.8933)
= $133.39
March 22, 2024 calculations
Top border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 + 2 × s)
= Exp(a + b × 1,780 + 2 × s)
= Exp(4.7250 + 0.0003 × 1,780 + 2 × 0.0679)
= Exp(5.3573)
= $212.15
Bottom border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 – 2 × s)
= Exp(a + b × 1,780 – 2 × s)
= Exp(4.7250 + 0.0003 × 1,780 – 2 × 0.0679)
= Exp(5.0858)
= $161.71
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.72% per annum.
- ZTS price at the close of May 7, 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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